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A2T Review of 1st Semester Trig. Name__________________ The Unit Circle Complete the unit circle in degrees, radians, and the associated coordinates. What is the equation of the unit circle? __________________ What are the three Pythagorean Identities derived from the equation above? __________________ ________________ ___________________ What are the three Reciprocal Identities? __________ __________ __________ Degrees and Radians 1. Convert each of the following to exact radians. a. °210 b. °− 225 c. °450 d. 18° 2. Convert each of the following to degrees.

a. 3

2π b. 12π

− c. 718π d. 13

30π

3. Determine the quadrant in which the terminal side lies for each angle.

a. 127π b.

32π

− c. 371˚ d. 5

14π

e. -156˚ f. 1000˚ g. 332˚ h. -240˚

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4. Find one positive angle and one negative angle that are coterminal with each angle.

a. 70˚ b. 5

2π− c. -300˚ d.

43π

5. Find the reference angle for each angle with the given measure. a. -20˚ b. 160˚ c. -545˚ d. 300˚ 6. Determine the exact value of each of the following:

a. 6

sin π b. 4

cosπ c. 6

tan π d. 2

cosπ

e. 2

3tan π f. 6

5cos π g. sin 0 h. πtan

i. 4

7sin π j. sin ⎟⎠⎞

⎜⎝⎛−

6π k. ⎟

⎠⎞

⎜⎝⎛−

3tan π l. π3sin

m. ⎟⎠⎞

⎜⎝⎛−

43cos π n.

25cos π o. ⎟

⎠⎞

⎜⎝⎛−

47tan π

p.

38sin π

\

q. 6

19cos π r. π4tan s. 6

25sin π t. ⎟⎠⎞

⎜⎝⎛−

37cos π

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7. Find all the exact values of θ for πθ 20 ≤≤ that make each of the following statements true.

a. 22cos =θ b. 0sin =θ c. 1tan =θ d.

21cos −=θ

e. 23sin =θ

f.

33tan −=θ g. 1cos −=θ h.

22sin −=θ

i. 3tan −=θ j. 0cos =θ k. 21sin −=θ l. 0tan =θ

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Right Triangle Trigonometry (Reference Angles)

sin θ =hypopp =

ry csc θ =

opphyp =

yr

cos θ = hypadj =

rx sec θ =

adjhyp =

xr opp hyp

tan θ = adjopp =

xy cot θ =

oppadj =

yx θ

adj Use the right triangles provided to find the exact value of each. 8. D a. sin D ______ 29 b. cos D ___ ___ 20 E = 90 ̊ c. tan F ______ d. cos F ______ E 21 F 9. A a. a ______ C = 90 ̊ b. m .A∠ ______ 8 17 c. m .B∠ ______ C B a 10. A string which runs form the top of a tent to a stake in the ground makes an angle of 50˚ with the ground. If the string is 8 ft. long, how high is the top of the tent?

11. A tree casts a shadow 25 ft. long when the measurement of the angle of elevation of the sun is 68˚. Find the height of the tree to the nearest foot.

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12. The angle of elevation to the top of a building is 35˚. 100 feet closer, the angle of elevation is 45˚. Find the height of the building to the nearest foot.

13. Attempting to scale a vertical cliff, Jeanie wants to learn its height. From a certain point 70 feet from the base she knows that the angle of elevation is 35˚. Find its height. 14. John views the top of a water tower at an angle of elevation of 36˚. He walks 120 meters in a straight line toward the tower. Then he sights the top of the tower at an angle of elevation of 51˚. How far is John from the base of the tower? 15. Two cities are 10 miles apart. An object is seen hovering in the sky above the line joining the two cities. The angles of elevation to the object are 24˚ and 40˚. What is the height of the object about the ground to the nearest tenth of a mile?

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Use the Law of Sines. 16. b = 41, A = 33˚, B = 29˚, find c. 17. b = 795, c = 700, and B = °51 , find m .C∠ 18. A = °38 , B = °63 and c = 15, find b.

19. a = 12.4, b = 16.2, A = 47˚, find m .B∠ Use the Law of Cosines. 20. Find m .C∠ a = 18, b = 10, c = 21 21. Find c. a = 10, b = 7, C = 38˚

Law of Sines

In any ΔABC with sides a, b and c opposite angles A, B

and C;

cC

bB

aA sinsinsin

==

C b a A c B

Law ofCosines

In any ΔABC with sides a, b and c opposite angles A, B

and C;

abbac 2222 −+= cos C

b A c C a B