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Name~~_I_~_V_)_t___~~_(._~~_____Integrated Trigonometry vJ ~Test (5.1-5.3) Review A

1. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)

47l' ~ '-I.[I~ O ()0 +'. 07 -;:-:. _ -: 10 2;:i ~ J..l­'I

2. Determine the quadrant in which the angle -4, given in radians, lies.

~cJ _S.'1'/ lt . \ ~I\ - '-I. !-.. ~ ~ .... - i-l. q . l8 D Tl ~.

3. Determine the quadrant in which an angle, e, lies if e= 5.40 radians.

4. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)

~ ~ -1 . <l ...--l-.­ \2fJ7 -., ~ :; -L S-. 7 \~

5. 7l'Determine a pair of coterminal angles (in radian measure) to the angle

::f t ll:?" "" r:"oj ~ 1T (l.-\\ 6~ \, l,J) -r:~ -

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6. Determine a positive angle and a ne ative angle (in radian measure) coterminal to the angle

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9

-- 7 (<i" rr ~"':-'-<', _ 1 - t- .... " --' ~'t q

7. Determine the quadrant in which the angle lies. 65°

8. Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle 101'.

I () ) IJ f "366 :; 4 aI ,:) / tJ /-S60

9. Rewrite the given angle in radian measure as a multiple of 7l'. (Do not use a calculator.) 90°

10. Rewrite the given angle in radian measure as a multiple of 7l'. (Do not use a cal'culator.)

-lW _ IVtJ' -]I 't 6

- - /b~jI - (-I'tD - - ' -­-~'(<S; t~- ,

11. , h I 27l' , dReWrite t e ang e - radians In egree measure.

~r';~ ~ ~~()~5

12. Convert the given angle measure from radians to degrees. Round to three decimal places. :: ·~:: .~;~,o~~ [t~. 460 13. Convert the given angle measure from radians to degrees. Round to three decimal places.

-349 - 3. '1'1. !W- ::; ( -IQ'1. % ~ 14.

, -8°12'52" -+-~t-JA

pv 'tL-) Ii'.- LA.\.c.

Convert the angle measure to decimal degree form.

15. Convert the angle measure to DOM 'S· form.

-232.7675· .., 2.> 2- 0

16. Find the angle, in radians, in the figure below if S = 11 and r = 6.

17. Find the radian measure of the central angle of the circle of radius 4 feet that intercepts an arc of length 26 feet.

S:;rB ~/; ~F(t9

18. Find the length of the arc on a circle of radius r intercepted by a central angle () .

radius: r = 5 feet central arc: () = Sa 4

s=r8 S ;; G' (~~)

19. Sa Find the radius of a circular sector with an arc length 26 feet and a central angle radians. Round your answer

4

to two decimal places. s=- (8 . . I '" ~ ,;r~J.~Yitu l+ B6fl S; W b~ tLi ~- f~

4/{"/T 20. Determifi~ the exact value of cos () .

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21. Determine the exact value of tanB .

12

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.... D .,...1)

>~

--(2­-­j~ '

I ')- J

----­~- ~w...-' -­5 .

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22 . 71L Find the point (x, y) on the unit circle that corresponds to the real number t. t=­

/0- -~\ 4

l 2- \ '2--) 23. ( ) 51LFind the point x,y on the unit circle corresponding to the real number t =-.

6

24 . 1L Evaluate the tangent of the real number t = --. -<3

3 --2. -\\ ..., -J:"'­

25. 41L Evaluate, if possible, the given trigonometric function at the indicated value. cot t, t =­

3

__ 2­Y... ... 2--- -\ _l6+ (~) -(

#j -'

-=(J "J-- -~ --~ - '{3" ~

2­26. 111L

Find the cosecant of the real number t=-. 6

l-27 . 71L

Find the cotangent (if it eXists) of the real number t = --. 4

-=- Cu-r { ~J ~ OJ 28. Evaluate the trigonometric function using its period as an aid. cos( 1~1L )

..­{q It 1~1r)- --'- ...--=-- ~S ® ~ [)CoS ( 3 '30

? 01 ~l\~ i\ • J

29. I h' . f . .. . d 'd ' ( 147rEva uate t e trigonometric unction uSing ItS perlo as an al . Sin --3­

(" , / "" IL.l1T' I ~:..]'\ _':> - (L-{ IIJ _ _ V :>/"-L -t' 3) - Sl "'- 3 -' ­

~ ~

30. Evaluate the trigonometric function using its period as an aid.

_'0 SIT ~ "rr\ (iT'\(')'()S ~ ,+ (g ) -:::J c:::PS <i Je -

31. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)

27r tan­

3

32. Evaluate sec(3.1). Round your answer to four decimal places.

-:=; _, \ () O()<t

33. Find the exact value of the given trigonometric function of the angle e shown in the figure. (Use the pythagorean Theorem to find the third side of the triangle.)

\S II

- a ~ IS b =8, C =17

34. Find the exact value of the given trigonometric function of the angle e shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) o-

a ]10

H

- \ --0­

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35 , 2 Given that sinO =-, find secO ,

5 ~ (Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle 0; then use the Pythagorean Theorem to determine the third side,)

I (ps-9S a,C e ~

~~ C;~)S­~";t,.. .--. " /'

91~. ">-- '5 G; {;l' G,,,~ce ..-.->J, +t? ­~--L4-~d..6" ~ "X,

x-=: ~ 36, 7

Given that cosO = -, find cscO,12

(Hint: Sketch a right triangle corresponding to ,the trigonometric function of the acute angle 0; then use the

Pythagorean Theorem to determine the third side,)

37. Given sin300 =~ and cos 30° =.J3 ,determine the following : sec 30° 2 ~ 2

.(j -~...... J- L

.,.,. ­$-e-c. 3b - C;:}S 36 -f3 - -r; .r; L

38. If sin x =~ and cos x =.J3 ,evaluate the following function, esc x 2 2

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