91Ó°ÊÓ

Convert the rectangular coordinates given for each point to polar coordinates \(r\) and \(\theta .\) Use radians, and always choose the angle to be in the interval \((-\pi, \pi)\). $$ (4,-4) $$

For Exercises 13-24, evaluate the indicated expressions assuming that \(\cos x=\frac{1}{3} \quad\) and \(\quad \sin y=\frac{1}{4}\), \(\sin u=\frac{2}{3} \quad\) and \(\quad \cos v=\frac{1}{5}\). Assume also that \(x\) and \(u\) are in the interval \(\left(0, \frac{\pi}{2}\right),\) that \(y\) is in the interval \(\left(\frac{\pi}{2}, \pi\right),\) and that \(v\) is in the interval \(\left(-\frac{\pi}{2}, 0\right)\). $$ \sin (x-y) $$

Convert the rectangular coordinates given for each point to polar coordinates \(r\) and \(\theta .\) Use radians, and always choose the angle to be in the interval \((-\pi, \pi)\). $$ (-5,5) $$

What is the period of the function \(4 \sin x ?\)

Convert the rectangular coordinates given for each point to polar coordinates \(r\) and \(\theta .\) Use radians, and always choose the angle to be in the interval \((-\pi, \pi)\). $$ (-6,-6) $$

For Exercises \(11-26,\) evaluate the given quantities assuming that \(u\) and \(v\) are both in the interval \(\left(0, \frac{\pi}{2}\right)\) and $$ \cos u=\frac{1}{3} \text { and } \sin v=\frac{1}{4} \text { . } $$ $$ \tan (2 v) $$

Find three distinct complex numbers \(z\) such that \(z^{3}=4 i\).

For Exercises 13-24, evaluate the indicated expressions assuming that \(\cos x=\frac{1}{3} \quad\) and \(\quad \sin y=\frac{1}{4}\), \(\sin u=\frac{2}{3} \quad\) and \(\quad \cos v=\frac{1}{5}\). Assume also that \(x\) and \(u\) are in the interval \(\left(0, \frac{\pi}{2}\right),\) that \(y\) is in the interval \(\left(\frac{\pi}{2}, \pi\right),\) and that \(v\) is in the interval \(\left(-\frac{\pi}{2}, 0\right)\). $$ \sin (u-v) $$

Suppose a triangle has sides of length \(a, b,\) and \(c\) satisfying the equation $$ a^{2}+b^{2}=c^{2} $$ Show that this triangle is a right triangle.

What is the period of the function \(-5 \sin x ?\)