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Algebra 2/Trigonometry Honors Name: Homework (14.2-14.3) Set A --- Coordinate Definitions and the Unit Circle 1. Refer to the figure. a. Find the value of y. b. Find cos . c. Find sin . 2. Given that 0 360 , find for each of the following. a. sin 1 b. sin 1 c. sin2 1 d. cos2 1 3. Find the exact value of each of the following. a. cos210 b. sin240 c. tan150 d. sec300 e. cot180 f. sin( 30 ) In problems 4-6, let (x, y) be a point on the terminal ray of , and let (x, y) be r units from the origin. 4. Find sin if x = 5 and r = 13. 5. Find cos if x = 8 and y = 15. 6. Find tan if x = 8 and r = 10. 7. Let (-7, 24) be a point on the terminal ray of an angle in standard position. Find the six trig functions of . 8. Solve for y, where a. 0 y 360 . tan2 y 1 9. Find all values of for which a. cos b. sec2 y 1 c. 360 360 and 2 2 b. tan 1 10. Find the exact coordinates of point Q. 11. If 0 360 , what values of satisfy each equation? a. cos c. 1 2 cos2 1 0 b. cos 2 d. 1 2 cos2 cos 0 sin y cos y 14.2-3 SET A - ANSWERS 1. a) 2 21 b) 2 c) 5 21 5 2. a) 90 b) 270 c) 90 or 270 d) 0, 180, or 360 3. a) 4. 12 13 5. 3 3 3 1 b) c) d) 2 e) Undefined f) 2 2 3 2 8 17 6. 3 4 7. sin 24 7 24 ;cos ;tan 25 25 7 8. a) 45, 135, 225, or 315 b) 0, 180, or 360 c) 45 or 225 9. a) -225, -135, 135, 225 b) -225, -45, 135, 315 10. ( 4, 4 3) 11. a) 60 or 300 b) 45, 135, 225, or 315 c) 0, 180, or 360 d) 0, 90, 270, or 360 Algebra 2/Trigonometry Honors Name: Homework (14.2-14.3) Set B --- Using the Calculator and Pythagorean Identities 1. Find each first-quadrant angle described. a. sin 0.3874 d. tan 4 3 b. cos 8 17 e. cos 1 10 c. sin f. 1 7 sin 1.342 2. Given that = 72, calculate each value to the nearest thousandth. a. sin b. cos (90 - ) c. tan d. cot (90 - ) 3. The area of triangle OAC is 5. Find each of the following. a. The coordinates of point C b. OC c. The coordinates of point B. d. mAOC 4. Find each value to the nearest thousandth. a. The coordinates of point A b. The area of triangle AOB 5. For each point on the unit circle, find the measure of the angle whose terminal ray passes through the point. a. (0, -1) c. 4 3 , 5 5 b. 2 2 , 2 2 d. (0.819, 0.573) 6. If cos = 0.695, what is the value of each of the following? a. sin b. tan c. sec 7. Let sec = 4.25. Find all possible values of such that 0 360. 8. Simplify each expression in terms of a single trig function. a. (1 sin )(1 sin ) sin2 cos2 b. sin 2 cos 2 9. Refer to the figure. a. Find cos , sin , and tan . b. Find the value of . 10. Find an expression in terms of a and b for each of the following. a. tan b. sin (180 - ) c. cos (360 - ) d. tan ( + 180) e. cos (180 + ) f. sin (360 - ) 11. Find the exact values of sec for which tan 12 . 13 c. 1 (sec ) cos cos 14.2-3 SET B - ANSWERS 1. a) 22.79, b) 61.93, c) 8.21, d) 53.13, e) 84.26, f) Impossible 2. a) 0.951 b) 0.951 c) 3.078 d) 3.078 3. a) (1, 10), b) 101 , c) ( 101 10 101 , ) , d) 84.29 101 101 4. a) ( 0.342, 0.940) b) 0.470 5. a) 270, b) 225, c) 323.13, d) 35 6. a) 0.719, b) 1.035, c) 1.439 7. 76.39 or 283.61 8. a) cos2 , b) sec2 , c) tan2 9. a) 6 85 7 85 7 ; ; , b) 130.60 85 85 6 10. a) b/a, b) b, c) a, d) b/a, e) –a, f) –b 11. 313 313 or 13 13