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Chapter 4: Problem 30
What angle corresponds to a circular arc on the unit circle with length \(1 ?\)
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Find exact expressions for the indicated quantities. \(\tan (u+8 \pi)\)
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.] \(\sin \frac{3 \pi}{8}\)
Find a formula for the perimeter of an isosceles triangle that has two sides of length \(c\) with angle \(\theta\) between those two sides.
Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$\tan u=-2 \text { and } \tan v=-3$$ Find exact expressions for the indicated quantities. \(\sin u\)
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.] \(\sin \frac{13 \pi}{12}\)
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