Trigonometry EOC Review Sheet 2013

1. Rewrite each angle in radian measure as a multiple of π .

A) 30 o = B) – 270o = C) 315o =

2. Find all angles between 0º and 360º or [ 0,2π], such that sec x = √2

3. If possible find the exact value of the first quadrant angles in radians and degrees.

A) 3 tan  = √3 B) 8cos = 4 C) 1/2 sin  = √3/4

4. Determine the reference angle and exact value for the following:

A) cos 135º B) sin 210º C) tan 315º

5. Determine the value of the following: (round to the nearest hundredth)

A) sec 217º B) cot 7.6º C) sin 23º

6. Find given tan  = -¾ and cos > 0

7. Write an equation for

A) sine function with Amp = 7 and period =

B) cosine function with Amp = 2 period = π/2

C) tangent function with Period of 2π

8. Write an equation for the following graph:

A) B)

9. Lebron decided to fill his pool on an early April morning. The height of the water at 9: 00am can be modeled by the equation y = 10sin ( π/6 t) where t is the time in hours and y is the height of the water in feet. What will the height be at 1:00 pm (or 4 hours later) ?

10. Your Frisbee landed at the top of the staircase that has an angle of elevation of 21º. If the stairs have a base height of 25 feet. How high up is your Frisbee?

21º

25 feet

11. An office building has a 17 foot cell phone tower on top of the roof. A passerby, standing 25 feet away from the base of the building, looks up at the top of the tower with an angle of elevation of 72°. What is the height of the building to the nearest foot?

12. An airplane is flying 10,500 feet above level ground. The angle of depression from the plane to the control tower is 20°. Find the horizontal distance of the plane to the control tower to the nearest foot.

13. Two ships left a harbor together traveling on courses that had an angle of 114.7° between them. One traveled at a rate of 39 mph, the other at a rate of 41 mph. After 3.5 hours, how far apart were the ships (distance)? Give answer to the nearest tenth of a mile.

14. A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 meters and 21.3 meters, and the angle between them is 42.2°. What is the area of the triangular lot to the nearest square foot?

15. Use the fundamental identities to determine the simplified form of the expression:

cot x sin x

16. If sin (3x - 15°) = cos (x + 25°), find x.

17. Perform the following quotient:

18. Julie has set up her tent at the campsite using two triangular sections as shown in the diagram below. AY is a support pole perpendicular to the ground. AX is 10 feet long and XY is 14 feet long, and angle Z is 32°. Find the length of side YZ to the nearest foot.

19. What is the magnitude of 3u – v, if u = 2i – 3j, and v = 6i – 4j?

20. You are given a vector with magnitude of 250 that is inclined 18° from the horizontal. Find the horizontal and vertical components of this vector. Give your answer in form.

21. Covert the Cartesian (rectangular) coordinates (2,2) to polar coordinates.

A. (4,)

B. ( 4, )

C. ( -4, )

D. (- 4,)

22.Convert the polar coordinates (12, ) to Cartesian (rectangular) coordinates.

A. ( 6, 6 )

B. ( 6, - 6 )

C. ( - 6, 6 )

D. ( - 6, - 6 )

23. Fill in the blank so that it is a true statement for all values of x : cos (-x) =

A. cos x

B. –cos x

C. sin x

D. – sin x

24.Express sin (-620o) as a trig function of an angle in quadrant I.

A. sin 260o

B. –sin 260o

C. sin 80o

D. – sin 80o

25.Let a = , and b = ,. Find the vector 3b – a.

A. ,

B. ,

C. ,

D. ,

26.If u = , and v = , evaluate u∙ (6v)

A. 22

B. 84

C. 156

D. 132

27.Write -3 + 3i in polar form

A. 6(cos 150o + isin 150o)

B. -6(cos 30o + isin 30o)

C. 6(cos 150o + isin 150o)

D. -6(cos 150o + isin 150o)

28.Write 8(cos 315o + isin315o)

A. 4i

B. - 4i

C. 4i

D. - 4i

29.Use DeMoivre’s Theorem to calculate (- – i)4

A. 4 - 16i

B. 4

C. 16 - 8i

D. -8 + 8i

30.Give the exact value of cos(arctan)

31.Give the exact value of tan(arcsin)

32.Use the trig identities to simplify: tan2x (cos2 x + cot2 x)

A. cot2 x + 1

B. sec2 x + 1

C. sin2 x + 1

D. sin4 x + 1

33.Use trig identities to simplify: cos2 x – 4 + sin2 x – 1 + 4 csc2 x

A. 4 cot2 x

B. -5

C. cot2 x + sin2 x + csc2 x

D. cot2 x + sin2 x + csc2 x – 5

34.A paper is cut into a triangle so that one side is 36 cm, another side is 20 cm, and the angle between the sides is 30o. Find the exact area of the piece of paper.

A. 180 cm2

B. 360 cm2

C. 180 cm2

D. 360 cm2

35. A triangular flower fed has sides of length 20 m, 30 m, and 42 m. Mark wants to purchase fertilizer and needs to calculate the area. Determine the area in square meters to the nearest tenth.

A. 112.2 m2

B. 158.7 m2

C. 276.7 m2

D. 391.3 m2

36. Use the sum or difference identities to determine the exact value of cos 165o.

D. -

37.Use the sum or difference identities to determine the exact value of sin 15o.

38.Determine which of the following is possible.

A. cos x = 4.21

B. cos x =

C. sec x = - .615

D. sec x =

39.Determine which of the following is impossible.

A. tan x = 0.00137

B. cot x = 9 x 104

C. csc x = 0.9373

D. sin x = 0.58367

Answer Trigonometry EOC Review Sheet

1. A) π / 6 B) -3π / 2 C) 7π / 4

2. π / 4 or 45º 7π / 4 or 315º

3. A) π /6 (30o) B) π / 3 (60o) C) π / 3 (60o)

4. A) ref. angle = 45º B) ref. angle = 30º C) ref. angle = 45º

- √2 / 2 -1/2 -1

5. A) sec 217º B) cot 7.6º C) sin 23º

≈ -1.25 ≈ 7.49 ≈ 0.39

6. sin Θ = -3/5

7. A) y = 7 sin  B) y= 2 co 4C) y = tan ½ 

8. A) y = 3 cos 8B) y = -2 sin

9. 8.66 ft.

10.9.6 ft

11. 60 feet

12. 28849 feet

13. 235.8 miles

14. 373 m2

15. cos x

16. 20o

17. - i

18. 18 feet

19. 5

20.

21. C

22. C

23. A

24. C

25. A

26. D

27. A

28. C

29. D

30. B

31. A

32. C

33. A

34. C

35. C

36. A

37. A

38. B

39. C