Stitz-Zeager_College_Algebra_e-book

Hint look at the diagram above a find the angle in

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Unformatted text preview: which is not in [0, 2π ). Hence, the four solu1 1 tions which lie in [0, 2π ) are x = 1 arcsin(0.87), x = 2 arcsin(0.87) + π , x = π 2 arcsin(0.87) 2 2 π and x = 32 − 1 arcsin(0.87). By graphing y = sin(2x) and y = 0.87, we confirm our results. 2 y = tan x 2 and y = −3 y = sin(2x) and y = 0.87 10.7 Trigonometric Equations and Inequalities 733 Each of the problems in Example 10.7.1 featured one trigonometric function. If an equation involves two different trigonometric functions or if the equation contains the same trigonometric function but with different arguments, we will need to use identities and Algebra to reduce the equation to the same form as those given in Example 10.7.1. Example 10.7.2. Solve the following equations and list the solutions which lie in the interval [0, 2π ). Verify your solutions on [0, 2π ) graphically. 1. 3 sin3 (x) = sin2 (x) 5. cos(3x) = cos(5x) √ 6. sin(2x) = 3 cos(x) 2. sec2 (x) = tan(x) + 3 7. sin(x) cos x + cos(x) sin 2 √ 8. cos(x) − 3 sin(x) = 2 3. cos(2x)...
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