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Chapter 4: Problem 35
Find the perimeter of an isosceles triangle that has two sides of length 6 and an \(80^{\circ}\) angle between those two sides.
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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.] \(\cos \frac{5 \pi}{12}\)
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. \(\sin (u-6 \pi)\)
Find the four smallest positive numbers \(\theta\) such that \(\cos \theta=-1\).
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.] \(\sin \frac{3 \pi}{8}\)
In doing several of the exercises in this section, you should have noticed a relationship between \(\cos u\) and \(\sin v,\) along with a relationship between \(\sin u\) and \(\cos v\). What are these relationships? Explain why they hold.
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