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Question 5.5.3: Finding an angle given its sine Let α be an angle such that ...

Finding an angle given its sine

Let α be an angle such that -90° < α < 90°. In each case, find α to the nearest tenth of a degree.

a. sin α = 0.88                  b. sin α = -0.27

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a. The value of \sin ^{-1}(0.88) is the only angle in [-90°, 90°]  with a sine of 0.88. Use a calculator in degree mode to get \alpha=\sin ^{-1}(0.88) \approx 61.6^{\circ}.

b. Use a calculator to get \alpha=\sin ^{-1}(-0.27) \approx-15.7^{\circ}

Figure 5.76 shows how to find the angle in part (a) on a graphing calculator and how to check. Make sure that the mode is degrees.

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