Convert from degrees to radians: (a)

$$1 ^ { \circ }$$

(b)

$$30 ^ { \circ }$$

(c)

$$25 ^ { \circ }$$

(d)

$$120 ^ { \circ }$$

Find the angle between $0$ and $2 \pi$ in radians that is coterminal with the given angle.

$$\frac{14 \pi}{5}$$

Find the measure in radians of the least positive angle that is coterminal with each given angle. $\frac{9 \pi}{2}$

The U.S. five-cent coin, the nickel, has a mass of 5.1 g, a volume of $0.719\ \mathrm{cm}^{3},$ and a total surface area of $8.54\ \mathrm{cm}^{2}.$ Assuming that a nickel is an ideal radiator, how much radiant energy per second comes from the nickel, if it is at $20^{\circ} \mathrm{C} ?$

Solve each equation ( $x$ in radians and $\theta$ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

$$\cot x+\sqrt{3}=0$$

The work $W$ done in moving an object from $(0,0)$ to $(7,2)$ subject to a force $\mathbf{F}$ is $W=\mathbf{F} \cdot \mathbf{r}$ where $\mathbf{r}$ is the vector with head at $(7,2)$ and tail at $(0,0)$. The units are feet and pounds. (a) Suppose the force $\mathbf{F}=10 \cos \theta \mathbf{i}+10 \sin \theta \mathbf{j}$. Find $W$ in terms of $\theta$. (b) Suppose the force $\mathbf{F}$ has magnitude $6 \mathrm{lbs}$ and makes an angle of $\pi / 6$ radian with the horizontal, pointing right. Find $W$ in feetlbs.

Express each angle measure in radians. Give answers in terms of $\pi$.

$$475^{\circ}$$

Convert the indicated angle from radians to degrees. a. $\frac{5 \pi}{6}$ b. $-\frac{\pi}{12}$

Find all solutions in radians. Approximate your answers to the nearest hundredth.

$$\tan (0.2 x-\pi)=-9$$

Solve the equation ( $x$ in radians and $\theta$ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. $\cos \theta+1=0$

In what month do people take the least number of daily vitamins?

Convert the degree measure to radians. If applicable, round to the nearest thousandth.

$$56^{\circ} 25^{\prime}$$

Find all solutions of

$$1 + 2 \sin \theta = 0 \text { where } \theta$$

is in radians.

Use each of the three terms below in a sentence that illustrates the meaning of the term. a. state bank b. national bank c. gold standard