TRIGONOMETRY ReviewChapter 2

Name: _________________________________ Block: _________ Date: __________________________

2.1 Trig Functions of Acute Angles

1. Find the exact values of sine, cosine, and tangent of angle A.

sin A=¿¿ cos A=¿¿ tan A=¿¿

2. Write each function in terms of its cofunction.a. cos38.7 ° b. csc(θ+23 °)

3. Find one solution for each equation. Assume all angles involved are acute angles.a. sin 4 B=cos5 B b. tan (5 x+11° )=cot (6 x+2 ° )

4. Determine whether each statement is true or false. Explain. a. sin 46 °<sin 58 ° b. sec58 °<c sc 47 °

5. Find the exact value of each part labeled with a variable in the figure.

y

30

Name: _________________________________ Block: _________ Date: __________________________

2.2 Trig Functions of Non-Acute Angles

6. Find the reference angle for each angle.a. 405° b. −1860 °

7. Find the exact values of the six trig functions for −855 °.

sin (−855 ° )=¿¿ csc (−855 ° )=¿¿

cos (−855° )=¿¿ sec (−855° )=¿¿

tan (−855° )=¿¿ cot (−855 ° )=¿¿

8. Find the exact value of each expression.a. cos1215 ° b. tan(−1020 °)

9. Find the exact value sec2300 °−2cos2150 °+ tan 45 °

Name: _________________________________ Block: _________ Date: __________________________

10. Find the values of θ, if θ is in the interval ¿ and has the given function value.

a. sin θ=−12 b. secθ=−√2

2.3 Find Trig Functions Using a Calculator

11. Approximate the value of each expression to the nearest ten thousandth.a. sin 72° 30 ' b. sec58.9041 °

12. Use a calculator to find an angle θ in the interval [0 ° ,90 ° ] that satisfies the given condition. Round to the nearest hundredth.

a. cosθ=.9754 b. cot θ=1.1249

13. The grade resistance F of an automobile traveling uphill or downhill is modeled by the equation F=W sin θ where W is the weight of the automobile.

a. What is the grade resistance of a 2100-lb car traveling on a 1.8° uphill grade?

b. A 3000-lb car traveling uphill has a grade resistance of 150 lb. What is the angle of the grade?

Name: _________________________________ Block: _________ Date: __________________________

2.4 Solving Right Triangles

14. Solve the right triangle.

15. Solve right triangle ABC if C=90 °, b=219 cm, and c=647 cm.

16. A 40-ft flagpole cast a 30-foot shadow. Find the angle of elevation of the sun to the nearest degree.

17. The angle of depression from a helicopter to its landing port is 64°. If the altitude of the helicopter is 1600 m, find the distance from the helicopter to the landing port to the nearest meter.

Name: _________________________________ Block: _________ Date: __________________________

2.5 Further Applications of Right Triangles

18. Two ships leave a port at the same time. The first ship sails on a bearing of 32 ° at 16 knots (nautical miles per hour) and the second one a bearing of 122 ° at 24 knots. How far apart are they after 2.5 hr?

19. A ship leaves a pier on a bearing of S 62 ° E and travels for 75 km. It then turns and continues on a bearing of N 28 ° E for 53 km. How far is the ship from the pier?

20. Find h as indicated in the figure.

21. An observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the point (−4 ,−4).

Name: _________________________________ Block: _________ Date: __________________________

Answer Key

1. sin A=4553 , cos A=28

53, tan A=45

28

2. a. sin 51.3 ° b. sec (67 °−θ)

3. a. B=10 b. x=7

4. a. True. The larger the angle, the larger the value of sine.

b. False. The larger the angle, the larger the value of secant.

5. w=20√3 , x=10√3 , y=10√3 , z=10√66. a. θ'=45 ° b. θ'=60 °

7. sin (−855 ° )=¿−√22

¿ csc (−855 ° )=−√2

cos (−855° )=¿−√22

¿ sec (−855° )=−√2

tan (−855° )=1 cot (−855 ° )=¿1¿

8. a. −√22

b. √3

9. 72 or 3 12

10. a. 210 ° ,330 ° b. 135 ° ,225 °

11. a. .9537 b. 1.9362

12. a. 12.74 ° b. 41.64 °

13. a. 66 lb b. 2.9 °

14. M=38.8 ° , n=154m , p=198m

15. A=70.2° ,B=19.8 ° , a=609cm

16. 53.1 °

17. 1780 m

18. 72 nautical miles

19. 92 km

20. 344 m

21. 225 ° due north, S 45 ° W