91Ó°ÊÓ

Sketch the graphs of the functions \(-5 \sin x\) and \(\sin (-5 x)\) on the interval \([-\pi, \pi]\) (use the same coordinate axes for both graphs).

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

Use the dot product to find the angle between the vectors (2,3) and (3,4) .

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

For Exercises \(5-12\) use the following figure (which is not drawn to scale): Find the value of \(\theta\) (in degrees) if \(a=6\), \(b=3\), the area of the triangle equals 5 , and \(\theta>90^{\circ} .\)

Find exact expressions for th indicated quantities. The following information will be useful:\(\cos 22.5^{\circ}=\frac{\sqrt{2+\sqrt{2}}}{2}\) and \(\sin 22.5^{\circ}=\frac{\sqrt{2-\sqrt{2}}}{2}\) ; \(\cos 18^{\circ}=\sqrt{\frac{\sqrt{5}+5}{8}}\) and \(\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}\). [The value for \(\sin 22.5^{\circ}\) used here was derived in Example 5 in Section 6.3; the other values were derived in Exercise 64 and Problems 101 and 102 in Section 6.3.] $$ \sin 37.5^{\circ} $$

Convert the polar coordinates given for each point to rectangular coordinates in the \(x y\) -plane. $$ r=12, \theta=\frac{11 \pi}{4} $$

Convert the polar coordinates given for each point to rectangular coordinates in the \(x y\) -plane. $$ r=13, \theta=\frac{8 \pi}{3} $$

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

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