· แบบฝึกหัดคณิตศาสตร์ ม.3 เล่ม 2 รายวิชาพื้นฐาน. กรุงเทพฯ: บริษัท ส านักพิมพ์เดอะบุคส์

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อัตราส่วนตรีโกณมิต ิ


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บันทึกเพิ่มเติม .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 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แบบฝึกเสริมทักษะท่ี 1 1. จากรูปสามเหลี่ยมมุมฉากที่ก าหนดให้ต่อไปนี้ จงหาอัตราส่วนตรีโกณมิติ ตามต าแหน่งมุมหลัก


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2. ถ้า sin A = 13

5 จงหาค่าของ cos A, tan A

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.............................................................................................................................................................................. 3. ก าหนดให้ sin = 0.6 จงหาค่าของ cos A และ tan A .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 4. ก าหนดให้ tan = 0.75 จงหาค่าของ sin , cos , cot , sec และ cosec .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 5. ถ้า 13 sin A = 5 จงหาค่าของ cos A, tan A .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 6.

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แบบฝึกเสริมทักษะท่ี 2

1. ถ้า tan A = 4

3 จงหาค่าของ sin A + cos A – cot A

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.............................................................................................................................................................................. 2. ถ้า sec A =

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17 จงหาค่าของ

( 1) A sin 2 + A cos2 .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. .............................................................................................................................................................................. (2) 1 + A tan2 - A sec2 .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. .............................................................................................................................................................................. (3) 1 + A cot2 - A cos 2ec .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. ...........................................................................................................................................................................3. ก าหนดให้ 5 sin A = 3 จงหาค่าของ .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. ..............................................................................................................................................................................


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( 2) Acot1

Acosec2

2

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.............................................................................................................................................................................. 4. ถ้า 5 sin A = 4 จงหาค่าของ ( 1) cos A sec A + tan A cot A .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. ..............................................................................................................................................................................

(2) A secA cosA cosecA sin

AcosAsin 22

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5. ถ้า cot A = 3

4 จงหาค่าของ A 2cos A sin

A cos3A5sin

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6. ในรูปสามเหลี่ยม ABC มี B̂ = 90 ให้ sin C = 13

5 จงหาค่าของ A cosec A sec

Acot Atan

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แบบฝึกเสริมทักษะท่ี 3

1. จงหาคา่ของ sin 60 - cos 30 .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. 2. จงหาค่าของ sin 45 cos 45 - sin 30 cos 60 .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. 3. จงหาค่าของ tan2 60 - tan2 30 .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ..............................................................................................................................................................................


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4. จงหาค่าของ tan2 60 + 4 cos2 45 + 3 2sec 30 .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. 5. จงหาคา่ของ cosec 60 sec 30 cot 60 cos 0 .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. 6. จงหาค่าของ

cosec3045cosec

sec60tan4530cot2

2

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.............................................................................................................................................................................. 7. จงหาค่าของ

60cot 30cot 1

30tan tan60

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สูตรเอกลักลักษณ์ทางตรีโกณ 1) θsin 2 + θcos2 = 1 2) 1 + θtan2 = θsec2 3) 1 + θcot 2 = θcosec2 จากสูตรเอกลักษณ์ทางตรีโกณมิติ สามารถปรับสูตรให้อยู่ในรูปผลต่างก าลังสองได้ ดังนี้ 4) θcos2 = (1 - θsin ) (1 + θsin ) 5) θsin 2 = (1 - θ cos ) (1 + θ cos ) 6) θtan 2 = ( θ sec - 1) ( θ sec +1) 7) 1 = ( θ sec - θtan )( θ sec + θtan ) 8) 1 = ( θ cosec - θcot )( θ cosec + θcot ) 9) θcot 2 = ( θ cosec -1 ) ( θ cosec +1 )

1. จงหาค่าของ θsin

θcos1

θcos

θsin-12

2

2

2

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2. จงหาค่าของ θcot

1 cosec

θtan

1 -sec2

2

2

2

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........................................................................................................................................................................... 3. ถ้า

Acot

1

cosA

1

Acot

1 -

cosA

1 = r จงหาค่าของ 1 + r + 432 rrr

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โจทย์ปัญหา เร่ือง ตรีโกณมิต ิ1. จากยอดหน้าผาแห่งหนึ่ง มองเห็นต้นไม้ต้นหนึ่งเป็นมุมก้ม 60 องศา ถ้าต้นไม้นี้อยู่ห่างจากเชิงผา 100 3 ฟุต จงหาความสูงของหน้าผา ........................................................................................................................................................................... .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. ......................................................................................................................................................................................................................................................................................................................................................... 2. นักเรียนคนหนึ่งยืนอยู่ห่างจากเสาธง 100 เมตร วัดมุมเงยของยอดเสาธงเท่ากับ 60 องศา เสาธงสูงเท่าไร ........................................................................................................................................................................... .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. ......................................................................................................................................................................................................................................................................................................................................................... 3. ชายคนหนึ่งยืนอยู่บนหลังคาตึกสูง 120 ฟุต มองเห็นรถยนต์คันหนึ่งบนถนนเป็นมุมก้ม 30 องศา อยากทราบว่ารถยนต์นั้นอยู่ห่างจากตึกก่ีฟุต ........................................................................................................................................................................... .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. .........................................................................................................................................................................................................................................................................................................................................................


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4. ชายคนหนึ่งยืนอยู่บนหน้าผาริมทะเลซึ่งสูงจากระดับน้ าทะเล 2,400 ฟุต มองเห็นเรือล าหนึ่งเป็นมุมก้ม 30 องศา จงหา (1) เรืออยู่ห่างจากหน้าผากี่ฟุต (2) เรืออยู่ห่างจากชายคนนั้นเป็นระยะทางก่ีฟุต ........................................................................................................................................................................... .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. ......................................................................................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................... .............................................................................................................................................................................. .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................. .........................................................................................................................................................................................................................................................................................................................................................


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บรรณานุกรม โชคชัย สิริหาญอุดม. (2555). แบบฝึกหัดคณิตศาสตร์ ม.3 เล่ม 2 รายวิชาพื้นฐาน. กรุงเทพฯ: บริษัท ส านักพิมพ์เดอะบุคส์ จ ากัด. ธวัชชัย บุญเลิศ . คู่มือเตรียมสอบคณฺตคิดเร็ว ม.ต้น (ม.1-2-3) ฉบับพิชิตข้อสอบและศึกษาต่อ. กรุงเทพฯ: SCIENCE X+CENTER.

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· แบบฝึกหัดคณิตศาสตร์ ม.3 เล่ม 2 รายวิชาพื้นฐาน. กรุงเทพฯ: บริษัท ส านักพิมพ์เดอะบุคส์