36Chapter 1•Right Triangle Trigonometry§1.5Notice that reflection around they-axis is equivalent to reflection around thex-axis (θmapstochar→−θ) followed by a rotation of 180◦(−θmapstochar→−θ+180◦=180◦−θ), as in Figure 1.5.7.xyθ−θrr(x,y)(x,−y)(−x,y)180◦−θrFigure 1.5.7Reflection ofθaround they-axis=180◦−θIt may seem that these geometrical operations and formulas are not necessary for evalu-ating the trigonometric functions, since we could just use a calculator. However, there aretwo reasons for why they are useful. First, the formulas work for any angles, so they areoften used to prove general formulas in mathematics and other fields, as we will see laterin the text. Second, they can help in determining which angles have a given trigonometricfunction value.Example1.27Find all angles 0◦≤θ<360◦such that sinθ=−0.682.Solution:Using the✄✂a0✁sin−1button on a calculator with
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