Learning Materials
Features
Discover
Chapter 4: Problem 13
Suppose \(-\frac{\pi}{2}<\theta<0\) and \(\cos \theta=\frac{4}{5} .\) Evaluate: (a) \(\sin \theta\) (b) \(\tan \theta\)
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
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. \(\sin u\)
Assume the surface of the earth is a sphere with radius 3963 miles. The latitude of \(a\) point \(P\) on the earth's surface is the angle between the line from the center of the earth to \(P\) and the line from the center of the earth to the point on the equator closest to \(P\), as shown below for latitude \(40^{\circ} .\) Cleveland has latitude \(41.5^{\circ}\) north. Find the radius of the circle formed by the points with the same latitude as Cleveland.
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.] \(\sin \frac{5 \pi}{12}\)
(a) Show that $$x^{3}+x^{2} y+x y^{2}+y^{3}=\left(x^{2}+y^{2}\right)(x+y)$$ for all numbers \(x\) and \(y\). (b) Show that $$ \begin{aligned} \cos ^{3} \theta+\cos ^{2} \theta \sin \theta &+\cos \theta \sin ^{2} \theta+\sin ^{3} \theta \\ &=\cos \theta+\sin \theta \end{aligned} $$
Show that $$\cos \left(x+\frac{\pi}{2}\right)=-\sin x$$ for every number \(x\).
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine