The equation Tan $\theta=1$ describes the counterclockwise angle through which a flywheel rotates in 1 millisecond. Through how many degrees has the flywheel rotated after 25 milliseconds?

Determine whether the triangle has no solution, one solution, or two solutions. Then solve the triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree.

$$A=45^{\circ}, a=15, b=18$$

Find the exact value of the function.

$$\sin 840^{\circ}$$

State the amplitude, period, phase shift, and vertical shift for the function. Then graph the function.

$$y=2 \cos \left(\theta+30^{\circ}\right)+3$$

State the amplitude, period, and phase shift for the function. Then graph the function.

$$y=\cos \left(\theta-45^{\circ}\right)$$

The terminal side of angle $\theta$ in standard position intersects the unit circle at the point P. Find $\cos \theta$ and $\sin \theta$.

$$P\left(\frac{20}{29},-\frac{21}{29}\right)$$

The terminal side of $\theta$ in the standard position contains the point. Find the exact values of the six trigonometric functions of $\theta$.

(-20,21)

Find the value. Write angle measures in degrees and radian.

$$\operatorname{Cos}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

Draw an angle with the given measure in the standard position.

$$305^{\circ}$$

The terminal side of angle $\theta$ in standard position intersects the unit circle at the point $P$. Find $\cos \theta$ and $\sin \theta$.

$$P\left(\frac{5}{13},-\frac{12}{13}\right)$$

The terminal side of $\theta$ in the standard position contains the point. Find the exact values of the six trigonometric functions of $\theta$.

(3,4)

Find the amplitude, if it exists, and the period of the function. Then graph the function.

$$y=\cot \frac{1}{2} \theta$$

Leo sells T-shirts at a local swim meet. It costs him $\$250$ to set up the stand and rent the machine. It costs him an additional $\$5$ to make each T-shirt, if he sells each T-shirt for $\$15$, how many T-shirts does he have to sell before he can make a profit?

$$F ~~ 10$$

$$G ~~ 15$$

$$H ~~ 25$$

$$J ~~ 50$$

The population of a certain habitat follows the function:

$$P(t)=\frac{16,300}{\left(1+17.5 e^{-0.065 t}\right)}$$

a. What is the maximum population?

b. When does the population reach 16,200?