Chapter Review 539 66. Complete the square to write the quadratic function f x x x 1 3 2 2 2 ( ) = − − in vertex form. 67. The figure shows two flywheels connected by a belt. If the 6-inch diameter flywheel spins at 2000 revolutions per minute, how fast does the 2.5-inch diameter flywheel spin? 68. Solve the formula A bh 1 2 = for h. 69. Given f x x x 2 3 2 ( ) = − and g x x4 3, ( ) = − determine where f x g x . ( ) ( ) ≤ 70. Find the difference quotient of f x x 2 3 9. ( ) = + 6 in. 2.5 in. Chapter Review Things to Know Definitions of the six inverse trigonometric functions π π = = − ≤ ≤ − ≤ ≤ − y x x y x y sin if and only if sin where 1 1, 2 2 1 (p. 473) π = = − ≤ ≤ ≤ ≤ − y x x y x y cos if and only if cos where 1 1, 0 1 (p. 476) π π = = −∞< <∞ − < < − y x x y x y tan ifandonlyif tan where , 2 2 1 (p. 478) π π = = ≥ ≤ ≤ ≠ − y x x y x y y sec if and only if sec where 1, 0 , 2 1 (p. 487) y x x y x y y csc if and only if csc where 1, 2 2 , 0 1 π π = = ≥ − ≤ ≤ ≠ − (p. 487) π = = −∞< <∞ < < − y x x y x y cot if and only if cot where , 0 1 (p. 487) Sum and Difference Formulas (pp. 511, 514, and 516) cos cos cos sin sin α β α β α β ( ) + = − cos cos cos sin sin α β α β α β ( ) − = + sin sin cos cos sin α β α β α β ( ) + = + sin sin cos cos sin α β α β α β ( ) − = − tan tan tan 1 tan tan α β α β α β ( ) + = + − tan tan tan 1 tan tan α β α β α β ( ) − = − + Double-angle Formulas (pp. 525 and 526) sin 2 2 sin cos θ θ θ ( ) = θ θ θ ( ) = − cos 2 cos sin 2 2 θ θ θ ( ) = − tan 2 2 tan 1 tan2 θ θ ( ) = − cos 2 2 cos 1 2 θ θ ( ) = − cos 2 1 2 sin2 Half-angle Formulas (pp. 528 and 530) α α = − sin 2 1 cos 2 2 α α = + cos 2 1 cos 2 2 α α α = − + tan 2 1 cos 1 cos 2 α α = ± − sin 2 1 cos 2 α α = ± + cos 2 1 cos 2 α α α α α α α = ± − + = − = + tan 2 1 cos 1 cos 1 cos sin sin 1 cos where the + or − sign is determined by the quadrant of α 2 . Product-to-Sum Formulas (p. 535) sin sin 1 2 cos cos α β α β α β ( ) ( ) [ ] = − − + cos cos 1 2 cos cos α β α β α β ( ) ( ) [ ] = − + + sin cos 1 2 sin sin α β α β α β ( ) ( ) [ ] = + + −
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