Cumulative Review 543 In Problems 21–28 use sum, difference, product, or half-angle formulas to find the exact value of each expression. 21. ° cos15 22. ° tan75 23. ( ) − sin 1 2 cos 3 5 1 24. ( ) − tan 2 sin 6 11 1 25. ( ) + − − cos sin 2 3 tan 3 2 1 1 26. ° ° sin75 cos15 27. ° + ° sin 75 sin15 28. ° ° + ° ° cos65 cos20 sin65 sin20 In Problems 29–33, solve each equation on θ π ≤ < 0 2 . 29. θ − = 4 sin 3 0 2 30. π θ θ ( ) − − = 3 cos 2 tan 31. θ θ θ θ + − = cos 2 sin cos sin 0 2 2 32. θ θ ( ) + = sin 1 cos 33. θ θ + = 4 sin 7 sin 2 2 1. Find the real solutions, if any, of the equation + − = x x 3 1 0. 2 2. Find an equation for the line containing the points ( ) −2, 5 and ( ) − 4, 1 . What is the distance between these points? What is their midpoint? 3. Test the equation + = x y 3 9 2 for symmetry with respect to the x-axis, y-axis, and origin. List the intercepts. 4. Use transformations to graph the equation = − + y x 3 2. 5. Use transformations to graph the equation = − y e3 2. x 6. Use transformations to graph the equation π ( ) = − − y x cos 2 1 7. Graph each of the following functions. Label at least three points on each graph. Name the inverse function of each and show its graph. (a) = y x3 (b) = y ex (c) π π = − ≤ ≤ y x x sin , 2 2 (d) π = ≤ ≤ y x x cos , 0 8. If θ = − sin 1 3 and π θ π < < 3 2 , find the exact value of: (a) θ cos (b) θ tan (c) θ ( ) sin 2 (d) θ ( ) cos 2 (e) θ ( ) sin 1 2 (f) θ ( ) cos 1 2 9. Find the exact value of ( ) − cos tan 2 . 1 10. If α π α π = < < sin 1 3 , 2 , and β π β π = − < < cos 1 3 , 3 2 , find the exact value of: (a) α cos (b) β sin (c) α ( ) cos 2 (d) α β ( ) + cos (e) β sin 2 11. Consider the function ( ) = − − + + − f x x x x x x 2 4 2 2 1 5 4 3 2 (a) Find the real zeros and their multiplicity. (b) Find the intercepts. (c) Find the power function that the graph of f resembles for large x . (d) Graph f using a graphing utility. (e) Approximate the turning points, if any exist. (f) Use the information obtained in parts (a)–(e) to graph f by hand. (g) Identify the intervals on which f is increasing, decreasing, or constant. 12. If ( ) = + + f x x x 2 3 1 2 and ( ) = + + g x x x3 2, 2 solve: (a) ( ) = f x 0 (b) ( ) ( ) = f x g x (c) ( ) > f x 0 (d) ( ) ( ) ≥ f x g x Cumulative Review
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