Basic Trigonometry 1

7/24/2019 Basic Trigonometry 1

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Basic

Trigonometry


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Parts of a Right Triangle

AAdjacent SideC

Opposite Side

B Hypotenuse

Imagine that you are at Angle A looking

into the triangle.

The adjacent side is the side next

to Angle A.

The opposite side is the side that is

on the opposite side of the triangle

from Angle A.

The hypotenusewill always be the

longest side, and opposite from the

right angle.


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Parts of a Right Triangle

AAdjacent SideC

Opposite Side

B Hypotenuse

Now imagine that you move from

Angle A to Angle .

!rom Angle the adjacent side is

the side next to Angle .

!rom Angle the opposite side is

the side that is on the opposite side

of the triangle.


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Review

"ypotenuse

"ypotenuse

#pposite $ide

Ad%a&ent $ide

A

B

!or Angle A

This is the #pposite $ide

This is the Ad%a&ent $ide

!or Angle

A

This is the Ad%a&ent $ide

This is the #pposite $ide

#pposite $ide

Ad%a&ent $ide

B


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Trig Ratios

'e &an use the lengths of the sides of aright triangle to form ratios. There are (different ratios that we &an make. Adjacent

OppositeHypotenuse

AC

B

Opposite

Hypotenuse

Adjacent

Hypotenuse

Opposite

Adjacent

)sing Angle A to name the sides

)se Angle to name the sides

The ratios are still the same as before!!


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Trig Ratios

* +a&h of the ( ratios has a name

* The names also refer to an angle

OppositeSine of Angle A = Hypotenuse

AdjacentCosine of Angle A =

Hypotenuse

OppositeTangent of Angle A =

Adjacent

"ypotenuse

Ad%a&ent

#ppositeA


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Trig Ratios

B

Opposite=Hypotenuse

Adjacent=

Hypotenuse

Opposite=

Adjacent

"ypotenuse

Ad%a&ent

#ppositeA

If the angle &hanges from A to

The way the ratios are made is the

same

B

B

B

Cosine of Angle

Sine of Angle

Tangent of Angle


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$#"A"T#A

Ad%a&entA

B

#pposite"ypotenuse

Here is a way to remember how

to make the 3 basic Trig Ratios

1 dentify the "pposite and Adjacent

sides for the appropriate angle

# $"H%AHT"A is pronounced &$ew %aw Toe A' and it means

$in is "pposite o(er Hypotenuse) %os is Adjacent o(er Hypotenuse)

and Tan is "pposite o(er Adjacent

*ut the underlined letters to make

$"H+%AH+T"A


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+xamples of Trig Ratios

Sin P

Cos P

-/

-01

P

Tan P Tan Q

Cos Q

Sin Q16

20=

1220

=

16

12=

12

20=

1620

=

12

16=

!irst we will find the $ine, osine and

Tangent ratios for Angle P.

Next we will find the $ine, osine, and

Tangent ratios for Angle 1#pposite

Ad%a&ent

Remember $oh%ahToa


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$imilar Triangles and Trig Ratios

ABC QPRV V

(2

3

A

-/

-0

1

P

R

They are similar triangles, sin&e

ratios of &orresponding sides are

the same

4et5s look at the ( basi& Trig

ratios for these trianglesTan Q

Cos Q

Sin Q12

20=

1620

=

12

16= Tan A

Cos A

Sin A

!=

"!

=

"=

,otice that these ratios are e-ui(alent!!


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$imilar Triangles and Trig Ratios

* Triangles are similar if the ratios of the

lengths of the &orresponding side are the

same.

* Triangles are similar if they have the same

angles

* All similar triangles have the same trig

ratios for &orresponding angles

Documents

Basic Trigonometry 1