91Ó°ÊÓ

Pror \(\theta=-5\) radians, evaluate each of the following: (a) \(\sin (2 \theta)\) (b) \(2 \sin \theta\) [This exercise and the next one emphasize that \(\sin (2 \theta)\) does not equal \(2 \sin \theta .]\)

Convert the polar coordinates given for each point to rectangular coordinates in the \(x y\) -plane. $$ r=4, \theta=\frac{\pi}{2} $$

For \(x=5.7\) radians and \(y=2.5\) radians, evaluate each of the following: (a) \(\sin (x-y)\) (b) \(\sin x-\sin y\) [This exercise and the next one emphasize that \(\sin (x-y)\) does not equal \(\sin x-\sin y .]\)

Find the area of a triangle that has sides of length 5 and 6 , with an angle of 2 radians between those sides.

For \(x=79^{\circ}\) and \(y=33^{\circ}\), evaluate each of the following: (a) \(\sin (x-y)\) (b) \(\sin x-\sin y\)

Convert the polar coordinates given for each point to rectangular coordinates in the \(x y\) -plane. $$ r=5, \theta=-\frac{\pi}{2} $$

P For \(\theta=100^{-}\), evaluate each of the following: (a) \(\sin (2 \theta)\) (b) \(2 \sin \theta\)

For \(\theta=6\) radians, evaluate each of the following: (a) \(\cos \frac{\theta}{2}\) (b) \(\frac{\cos \theta}{2}\) |This exercise and the next one emphasize that no

Suppose \(\mathbf{u}=(2,1)\) and \(\mathbf{v}=(3,1)\) (a) Draw a figure illustrating the sum of \(\mathbf{u}\) and \(\mathbf{V}\) as arrows. (b) Compute the sum \(\mathbf{u}+\mathbf{v}\) using coordinates.

Convert the polar coordinates given for each point to rectangular coordinates in the \(x y\) -plane. $$ r=6, \theta=-\frac{\pi}{4} $$