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Question 5.5.5: Finding an angle given its cosine In each case find the angl...

Finding an angle given its cosine

In each case find the angle α to the nearest tenth of a degree, given that 0° < α < 180°.

.a. cos α = 0.23                         b. cos α = -0.82

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a. Since \cos ^{-1}(0.23) is the unique angle in [0°, 180°] with a cosine of 0.23, \alpha=\cos ^{-1}(0.23) \approx 76.7^{\circ}

b. Use a calculator to get \alpha=\cos ^{-1}(-0.82) \approx 145.1^{\circ}

Figure 5.78 shows how to find \cos ^{-1}(0.23) on a graphing calculator and how to check. Make sure that the mode is degrees.

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