91Ó°ÊÓ

Use the dot product to find the angle between the vectors (3,-5) and (-4,3) .

Evaluate \(|4-3 i|\).

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

Find the area of a parallelogram that has pairs of sides of lengths 6 and 9 , with an angle of \(81^{\circ}\) between two of those sides.

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 \(\left(-\frac{\pi}{2}, 0\right)\). $$ \cos (x+y) $$

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 $$ \cos u=\frac{1}{3} \text { and } \sin v=\frac{1}{4} \text { . } $$ $$ \tan u $$

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 $$ \cos u=\frac{1}{3} \text { and } \sin v=\frac{1}{4} \text { . } $$ $$ \tan v $$

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 \((-\pi, \pi)\). $$ (-\sqrt{3}, 0) $$

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

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 \(\left(-\frac{\pi}{2}, 0\right)\). $$ \cos (u+v) $$