Download Review Questions for Final Exam - Plane Trigonometry | MA 133 and more Study notes Trigonometry in PDF only on Docsity! MA 133 Review for Final NOT COLLECTED 1. Convert 35° 27’13” to decimal degrees, rounding to three places. 2. Convert 89.234° to degree-minutes-seconds. 3. Convert 159° to radians. 4. Convert 1.79 radians to decimal degrees 5. Find the length of an arc subtended by an angle of 84° in a circle with a diameter of 10 cm. 6. Find the radius of a circle if a central angle of 37.2° subtends an arc of 26 inches. 7. Find the angle in decimal degrees, with 0° θ < 360° a. tan θ = 3.752, θ in QIII b. cos θ = - 0.5 (give all possible values of θ) 8. Solve (i.e. give the missing measures for) the right triangle ABC with ∠ C = 90° and a. ∠ B = 11°, a = 8 ft. b. ∠A = 15°, c = 10 cm c. a = 10 ft, b = 18 ft d. a = 7 yds, c = 10 yds 9. In a circle of radius 10.0 ft, find the length of the arc subtended by a central angle of 59.3°. 10. In a circle of diameter 25 m, find the radian measure of an angle subtended by an arc of length 100 m. 11. Find the area of a sector in a circle with a radius of 50 ft, and a central angle of 3.0 radians. 12. Find EXACT values of the six trigonometric functions for an angle θ with the given point on the terminal side. a. ( )3,1 − b. − 2 1 , 2 3 13. Draw each angle in standard position and find the reference angle -220° 210° 5π / 6 4π/3 14. Draw the angle in standard position and find the exact values for the following sin ( π / 4) sec (4π/3) tan (3π/2) 15. Find all the angles θ with 0 ≤ θ < 2π for which cot θ is undefined; for which tan θ is undefined 16. For each of the following functions, give the amplitude, period, phase shift, vertical shift, and graph over the indicated interval. A. ππ ≤≤ −+−= xoverxy 0 2 3cos32 b. ( )xy πsin31+= over one complete cycle c. += 4 2cos4 π xy over one complete cycle d. ( ) 31sin ≤≤−= xoverxy π 17. Simplify each of the following expressions: Give your answer in radians. Assume angles are in QI. A. − 3 5 sin 1 , angle in QII B. ( )1tan 1 −− , angle in QIV 18. Simplify each of the following expressions. Assume angles are in QI. a. − 5 3 costan 1 b. − x 1 sincos 1 19. Use the standard formulas to find exact values for each of the following Give your answer as a simplified fraction. Radicals in the denominator are acceptable. a.. cos 15° b. sin 105° 20. Let sin A = -4/5 with A in QIII and cos B = 5/13 with B in QIV to find a. sin (A + B) b. cos 2B c. 2 sin A d. cos ( A – B)
