753 7.7 Equations Involving Inverse Trigonometric Functions Chapter 7 Quiz (Sections 7.5 – 7.6) 1. Graph y = cos-1 x, and indicate the coordinates of three points on the graph. Give the domain and range. 2. Find the exact value of each real number y. Do not use a calculator. (a) y = sin-1 ¢- 22 2 ≤ (b) y = tan-1 23 (c) y = sec-1 ¢- 223 3 ≤ 3. Use a calculator to approximate each value in decimal degrees. (a) u = arccos 0.92341853 (b) u = cot-11-1.08867672 4. Evaluate each expression without using a calculator. (a) cos atan-1 4 5b (b) sin acos-1 a- 1 2b + tan-1 A -23 B b Solve each equation for exact solutions over the interval 30°, 360°2. 5. 2 sin u - 23 = 0 6. cos u + 1 = 2 sin2 u 7. (Modeling) Electromotive Force In an electrical circuit, suppose that V = cos 2pt models the electromotive force in volts at t seconds. Find the least value of t where 0 … t … 1 2 for each value of V. (a) V = 1 (b) V = 0.30 Solve each equation over the interval 30, 2p2. Write solutions as exact values or to four decimal places, as appropriate. 8. tan2 x - 5 tan x + 3 = 0 9. 3 cot 2x - 23 = 0 10. Solve cos x 2 + 23 = -cos x 2 , giving all solutions in radians. 7.7 Equations Involving Inverse Trigonometric Functions ■ Solution for x in Terms of y Using Inverse Functions ■ Solution of Inverse Trigonometric Equations Solution for x in Terms of y Using Inverse Functions EXAMPLE 1 Solving an Equation for a Specified Variable Solve y = 3 cos 2x for x, where x is restricted to the interval C 0, p 2 D . SOLUTION We want to isolate cos 2x on one side of the equation so that we can solve for 2x, and then for x. y = 3 cos 2x y 3 = cos 2x Divide by 3. 2x = arccos y 3 Definition of arccosine x = 1 2 arccos y 3 Multiply by 1 2 . An equivalent form of this answer is x = 1 2 cos-1 y 3 . Our goal is to isolate x.
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