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Chapter 4: Problem 18
What is the angle between the hour hand and the minute hand on a clock at \(7: 15 ?\)
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The next two exercises emphasize that \(\cos ^{2} \theta\) does not ?qual \(\cos \left(\theta^{2}\right)\) For \(\theta=7^{\circ},\) evaluate each of the following: (a) \(\cos ^{2} \theta\) (b) \(\cos \left(\theta^{2}\right)\)
The next two exercises emphasize that \(\cos ^{2} \theta\) does not ?qual \(\cos \left(\theta^{2}\right)\) For \(\theta=5\) radians, evaluate each of the following: (a) \(\cos ^{2} \theta\) (b) \(\cos \left(\theta^{2}\right)\)
Given that $$\cos 15^{\circ}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin 22.5^{\circ}=\frac{\sqrt{2-\sqrt{2}}}{2}$$ Find exact expressions for the indicated quantities. [These values for \(\cos 15^{\circ}\) and \(\sin 22.5^{\circ}\) will be derived in Examples 3 and 4 in Section 5.5.] \(\sec 15^{\circ}\)
In Exercises 5-38, find exact expressions for the indicated quantities, given that $$\cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2}$$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived in Examples 3 and 4 in Section 5.5.] \(\tan \left(-\frac{5 \pi}{12}\right)\)
Assume the surface of the earth is a sphere with diameter 7926 miles. Approximately how far does a ship travel when sailing along the equator in the Pacific Ocean from longitude \(170^{\circ}\) west to longitude \(120^{\circ}\) west?
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