Find the area of a sector of a circle having radius $r$ and central angle $\theta$. See the example in this section.

$$r=18.3 \mathrm{~m}, \theta=125^{\circ}$$

A ship leaves its home port and sails on a bearing of $\mathrm{S} 61^{\circ} 50^{\prime} \mathrm{E}$. Another ship leaves the same port at the same time and sails on a bearing of $\mathrm{N} 28^{\circ} 10^{\prime} \mathrm{E}$. If the first ship sails at 24.0-mph and the second ship sails at 28.0-mph, determine the distance between the two ships after 4-hr.

Suppose an arc of length $s$ lies on the unit circle $x^2+y^2=1$, starting at the point $(1,0)$ and terminating at the point $(x, y)$. Use a calculator to find the approximate coordinates for $(x, y)$. (Hint: $x=\cos s$ and $y=\sin s$.)

$$s=3.4$$

A bicycle has a tire 26 inches in diameter that is rotating at 15 radians per second.

Approximate the speed of the bicycle in feet per second and in miles per hour.

Write the expression in terms of its cofunction.

$$\cos 1$$

Find the exact values of the six trigonometric functions of the angle $\theta$.

Suppose an arc of length s lies on the unit circle $x^2+y^2=1$, starting at the point (1,0) and terminating at the point (x, y). Use a calculator to find the approximate coordinates for (x, y).

$$s=3.4$$

Find the exact values of the six trigonometric functions of the angle $\theta$ for the of the two triangles. Explain why the function values are the same.

Find the exact values of the six trigonometric functions of the angle $\theta$.

Evaluate the right triangle where $C=90^{\circ}$. $a=76.4 \mathrm{yd}, b=39.3 \mathrm{yd}$

Suppose an arc of length s lies on the unit circle $x^2+y^2=1$, starting at the point (1,0) and terminating at the point (x, y). Use a calculator to find the approximate coordinates for (x, y).

$$s=-7.4$$

Suppose an arc of length $s$ lies on the unit circle $x^2+y^2=1$, starting at the point $(1,0)$ and terminating at the point $(x, y)$. Use a calculator to find the approximate coordinates for $(x, y)$. (Hint: $x=\cos s$ and $y=\sin s$.)

$$s=-3.9$$

Identify the quadrant (or possible quadrants) of an angle $\theta$ that satisfies the given conditions. cos $\theta$>0, sec $\theta$>0

Use the formula $v=r \omega$ to find the value of the missing variable.

$$r=24.93215 \mathrm{~cm}, \omega=.372914 \mathrm{~radian~per~sec}$$