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Radians, Arc Length and Unit Circle old exam questions nice

June 2015

Question 1 2 marks

Use the informationin the diagram to determinethe value ofthe are length “s”, given the central

angle of 56°.

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Question 9 ey 1 mark

Sketch the angle —320° in standard position.

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Question 15 1 mark

The point P(@) lies on the unit circle. Whatare the coordinates of the point P if @=120°?

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Question 29 ~ ou" 1 mark

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Determine the coterniunal ve with a overthe interval [-2n. 4n].

Question 42 2 marks

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a, AO ee:Given that cot@= ee where @ is in Quadrant IV, determine the exact value ofsin @ = ss

cote= x c:

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Question 1 a

13 ~ br (sy\Convert — —— to degrees. ctgei el eet

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Question6 28

LaF1 mark

Determine the arc length subtended by a central angle if the diameter is 19 cm and the central

angle is 1.6 radians. = x ‘ 14

ae Y\=)Il" a4), coe ,Question 17 yy Wy ver - = 1S- 21mark

Lite; iA co-terminal angle for = —— in the domain —2% < @ < 0 would be:

Question 23 1 mark

The point P(@) lies on the unitcircle, What are the coordinates ofthe point if @ = 300°?

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atQuestion 39 2 marks

iat Sn TeEvaluate and simplify see( r . wan(-2],

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June 2014

Question 1 ay 2 marks

Use the information in the diagramto determine the value ofthe arc length “s”,-S =. {30° (= \ as)

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Question 7 2 marks

ss 3 : aIf @ terminates in quadrant Il and esc @ = 5° determine the exact value of tan @, AN & = ee

C$ce =. of sho = = a

5 : J‘ * ‘: Ox 4 +b .Question 30 © a\2

J< = b 5 = \2hw

Determine one positive and one negative cotenninalangle with the angle ae ‘ve

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: 2 marks

‘S33Question 31 KO ts

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Evaluate: a“

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ee ae 6f / ;

de\] = \ — \

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Question 38 1 mark

, f PROD: ro \

ce Bs ae i (BON eal ne SB at “The pout dotsIs the point

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—. -——

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onthe unit circle? | | Sores aie) Ay.

4 : ) nok sahk&y treJustify your answer. No* 1 + oes esvanie of 2

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January 2014

Question 1.4% 2 marks

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Find the coterminal angle to ae overthe interval | -360 0 ) A427 — 360-360-360

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Question 9 1 mark

Sketchthe angle of 5 radians in standard position.

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Question 18 a 1 marker :

Given the point A(—3. 5) on the terminal armof an angle @. identify the value of cot@. = —%

2en 3 5 4 5nas By tS ears a)2) 5 ) 3 a 5 , =

Question 37 3 marks

we At. FTEvaluate: co sas

cottmunct 3nef 2 + sin? = + cos232 ro Ress 4 3 %

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June 2013 eG

Question 1ae 2 marks

SS = oRA central angle of a circle subtends an arc length of Sx cm,Giventhe circle has a radius of 9 cm,find the measure ofthe :aii angle in degrees, \

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Question 14 1 mark

eos . aAngle @ measuring —,is drawnin standard positiogss shown below.a + [Y s2iry 4

Determine the measures ofall angles in the interval [—4x. 2n| that are coterminal with @.

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Question 18 1 mark

Whichone of the following angles terminates in Quadrant II]?

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a) 3 radians (¢) -210 | d) 500°ANi eA eS oe wt Ww

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Question 27 2 marks

Explain howto find the exact value of see{2

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Question 32 Tye ualue Of cosine © WW is ° Oh Wienaades

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The terminal armof an angle @, in standard position, intersects the unit circle in QuadrantIVat

5 f : cea point (% ‘| Determineavalue of sin8@.

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Question 7 4 es ue ihe fx oe38

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“|A studentis using the formula s = Or to find an are length of a circle. Given a central angle

measure of 35° and

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radius of 6 cm. the student’s solution is as follows:

s =(35)(6)

s= 210 cm

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Explain whythis solutionis incorrect. aes as’ becae La Preasict

Write the correct solution.

Question 14 2 marks

Your classmate, Leo, was absent for one ofhis math lessons.

Explain to Leo howto determine the cosecantratio for an angle in standard position given that

P(—3, —4) is a point onthe terminal arm ofthe angle.60 $e cart ts ae CS Vpn c BE al Sine |

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1 mark

Question 43 1 mark

Wm. BeDraw the angle ~—— in standard position. L

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Question 49 3 marks

Find the exact value ofthe following expression: euA (-=(=

(4) (*) ( sn) ae oes 3gin{ —— » sec] -—— « tan| ——— ee

3 3 6 eee

f 4

AD aae)2 | a) a4

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Consider the are drawn oneachcircle. Which are measureis closest to 3 radians? Ba clan on

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