Find the angle (round to the nearest degree) between the pair of vectors: $\newline$ $\langle{6, 5\rangle}$ and $\langle{3, - 2\rangle}$

Solve each equation for exact solutions over the interval $[0,2 \pi)$. cos 2x+cos x=0

Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed $\omega$. For the given values of $r, \omega$, and $t$, find each of the following.

(a) the angle generated by $P$ in time t

(b) the distance traveled by $P$ along the circle in time $t$

(c) the linear speed of $P$

$r=20 \mathrm{~cm}, \omega=\frac{\pi}{12}$ radian per sec, $t=6 \mathrm{sec}$

Approximate the area of a sector of a circle having radius r and central angle $\theta$.

r=12.7 centimeters; $\theta=81^{\circ}$

Find the area of the sector of a circle of radius $r$ and central angle ${\theta}$.

Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure, and the given point is on the terminal side of $\theta$. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. (-5, 0)

Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure, and the given point is on the terminal side of $\theta$. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. (-4, 0)

Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure, and the given point is on the terminal side of $\theta$. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. (0, 2)

Two gears are adjusted so that the smaller gear of radius $3.7$ cm drives the larger one of radius $7.1$ cm. If the smaller gear rotates through an angle of $300^{\circ}$, through how many degrees does the larger gear rotate?

Two gears are calibrated so that the smaller gear drives the larger gear. For each rotation of the smaller gear, how many degrees will the larger gear rotate?

Solve the below triangle:

$$b=6, c=13, \alpha=16^{\circ}$$

The government's budget surplus in Macroland has risen consistently over the past five years. Two government policy makers disagree as to why this has happened. One argues that a rising budget surplus indicates a growing economy; the other argues that it shows that the government is using contractionary fiscal policy. Can you determine which policy maker is correct? If not, why not?

Find the cube roots of each complex number: Leave the answers in trigonometric form. Then graph each cube root as a vector in the complex plane.

$$-64$$

Two sides and an angle are given below. Determine whether a triangle (or two) exist and, if so, solve the triangle.

$$b=2, c=3, \gamma=165^{\circ}$$