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Review Exercise Set 4 Exercise 1: If the point (-3, 7) is a point on the terminal side of angle θ then find the exact value of each of the six trigonometric functions of θ. Exercise 2: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ. cos θ = Exercise 3: 3 and sin θ < 0 7 Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ. = cot θ 3 and cos θ < 0 Exercise 4: Use reference angles to find the value of the given expression. cos 495° Exercise 5: Find the exact value of the given expression. Write the answer as a single fraction. 5π 5π cos cot 3 6 3π + sin 4 Review Exercise Set 4 Answer Key Exercise 1: If the point (-3, 7) is a point on the terminal side of angle θ then find the exact value of each of the six trigonometric functions of θ. Graph the point to get a visual picture of the problem Find the length of the hypotenuse "r" 2 r= x2 + y 2 = ( −3) + ( 7 ) 2 2 = 9 + 49 = 58 r = 58 Find the value of the trig functions sin θ = y r = 7 58 = 7 58 58 csc θ = = x r −3 = 58 cos θ = = − sec θ = r y r x 58 −3 58 = − 3 = 58 7 3 58 58 y x 7 = −3 7 = − 3 tan θ = x y −3 = 7 3 = − 7 cot θ = Exercise 2: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ. 3 and sin θ < 0 7 cos θ = Graph the angle θ based on the given conditions to get a visual picture of the problem Find the length of the side "y" 2 r= x2 + y 2 ( 7= ) ( 3) 2 2 + y2 49= 9 + y 2 40 = y 2 − 40 = y −2 10 = y Remember since the point is in the fourth quadrant y must be negative. Find the value of the remaining trig functions y r −2 10 = 7 2 10 = − 7 sin θ = x r 3 = 7 cos θ = tan θ = y x −2 10 3 2 10 = − 3 = Exercise 2 (Continued): csc θ = = r y 7 −2 10 = − Exercise 3: r x 7 = 3 sec θ = 7 10 20 cot θ = = x y −3 −2 10 = − 3 10 20 Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ. cot θ 3 and cos θ < 0 = Graph the angle θ based on the given conditions to get a visual picture of the problem Since cosine is negative and cotangent is positive x and y must both be negative which would put the angle in the third quadrant. −3 x = −1 y cot θ= 3= Find the length of the hypotenuse "r" 2 r= x2 + y 2 = ( −3) + ( −1) 2 = 9 +1 = 10 r = 10 2 Exercise 3 (Continued): Find the value of the remaining trig functions y r −1 = 10 sin θ = = − csc θ = 10 10 r y 10 −1 = − 10 = Exercise 4: x r −3 = 10 cos θ = = sec θ = y x −1 = −3 1 = 3 tan θ = −3 10 10 r x x y −3 = −1 =3 cot θ = 10 −3 10 = − 3 = Use reference angles to find the value of the given expression. cos 495° Find a positive coterminal angle that is less than 360° 495° - 360° = 135° Determine the quadrant where this coterminal angle is located 135° is between 90° and 180° so it is located in quadrant II Find the reference angle Since the coterminal angle is in quadrant II we will subtract it from 180° to find the reference angle. 180° - 135° = 45° Find the value of the expression using the reference angle Cosine is negative in quadrant II so we would place a negative sign in front of the function cos 495° = -cos 45° Exercise 4 (Continued): Exercise 5: cos 495° = − 1 2 = − 2 2 Find the exact value of the given expression. Write the answer as a single fraction. 5π 5π 3π cos cot + sin 3 6 4 5π 5π cos cot 3 6 3 2 3π + sin = 4 ( 3) + 3 2 + 2 2 3+ 2 = 2 = 2 2