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PRECALCULUS HONORS TEST REVIEW 5.4—5.5 Find the exact value of the sine, cosine, and tangent of the angle by using a sum or difference formula. 1. 25π 11π π = + 12 6 4 Write the expression as the sine, cosine, or tangent of an angle. 2. sin60o cos 45o − cos60osin 45o Find the exact value of the trigonometric function given that sin u = (Both u and v are in Quadrant II.) 3. sin(u − v) 3 5 and cos v = − . 4 13 4. tan(u + v) Verify the identity. ⎛π ⎞ 5. cot ⎜ − x ⎟ = tan x ⎝2 ⎠ 6. sin(α + β ) = tan α + tan β cos α cos β Find all solutions of the equation in the interval [0, 2π). π⎞ π⎞ ⎛ ⎛ 7. sin ⎜ x + ⎟ − sin ⎜ x − ⎟ = 1 ⎝ ⎝ 6⎠ 6⎠ Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. 8. cosu = − 2 π , <u <π 5 2 Use double-angle formulas to verify the identity algebraically. 9. sin 4x = 8cos3 xsin x − 4 cos xsin x Use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. 10. cos2 3x 11. sin2 x tan2 x Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. 12. 15o Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas. 2 13. cosu = − , 7 π 2 <u <π Use the half-angle formulas to simplify the expression. 14. sin 6x 1 + cos 6x Use the product-to-sum formulas to write the product as a sum or difference. π π 15. 3cos sin 6 6 Use the sum-to-product formulas to write the sum or difference as a product. π⎞ π⎞ ⎛ ⎛ 16. cos ⎜ x + ⎟ − cos ⎜ x − ⎟ ⎝ ⎝ 4⎠ 4⎠ 17. A baseball leaves the hand of the person at first base at an angle of θ with the horizontal and at an initial velocity of v0 = 80 feet per second. The ball is caught by the person at 1 2 second base 100 feet away. Find θ if the range r of a projectile is r = v0 sin 2θ . 32 18. Determine whether the statement is true or false. Justify your answer. sin(x + y) = sin x + sin y .