Stitz-Zeager_College_Algebra_e-book

These identities were rst hinted at in exercise 8 in

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Unformatted text preview: re formally study of trigonometric equations in Section 10.7. Enjoy these relatively straightforward exercises while they last! 10.2 The Unit Circle: Cosine and Sine 623 Example 10.2.5. Find all of the angles which satisfy the given equation. 1. cos(θ) = 1 2 2. sin(θ) = − 1 2 3. cos(θ) = 0. Solution. Since there is no context in the problem to indicate whether to use degrees or radians, we will default to using radian measure in our answers to each of these problems. This choice will be justified later in the text when we study what is known as Analytic Trigonometry. In those sections to come, radian measure will be the only appropriate angle measure so it is worth the time to become “fluent in radians” now. 1. If cos(θ) = 1 , then the terminal side of θ, when plotted in standard position, intersects the 2 1 Unit Circle at x = 2 . This means θ is a Quadrant I or IV angle with reference angle π . 3 y y 1 1 π 3 1 2 1 2 x 1 x π 3 1 One solution in Quadrant I is θ = π , and since all other Quadrant I solutions must be 3...
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