Trigonometric Functions

Find the length of the arc subtended by a central angle of $30°$ on a circle of radius $2$ feet. What is the area of the sector?

For what numbers $\theta ,f\left(\theta \right)=cosec\left(\theta \right)$ does not exist

What is the formula for the circumference $C$ of a circle of radius $r$ ? What is the formula for the area $A$ of a circle of radius $r$ ?

If a particle has a speed of r feet per second and travels a distance d (in feet) in time t (in seconds), then $d=\_\_\_\_$.

If a particle has a speed of $r$ feet per second and travels a distance $d$ (in feet) in time $t$ (in seconds), then $d=\_\_\_\_\_\_\_$ .

An angle $\theta$ is in ________  _________ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

A __________ __________ is a positive angle whose vertex is at the center of  a circle.

If the radius of a circle is $r$ and the length of the arc subtended by a central angle is also $r$, then the measure of the angle is $1\_\_\_\_\_\_\_$.

On a circle of a radius $r$,a central angle of $\theta$ radians subtends an arc of length $s=\_\_\_\_\_\_\_\_$ ; the area of the sector formed by this angle $\theta$ is $A=\_\_\_\_\_\_\_\_$.

$180°=\_\_\_\_\_\_\_$ radians .

An object travels around a circle of radius $r$ with constant speed. If $s$ is the distance traveled in time $t$ around the circle and $\theta$ is the central angle (in radians) swept out in time $t$ , then the linear speed of the object is $v=\_\_\_\_\_\_\_\_$ and the angular speed of the object is $w=\_\_\_\_\_\_\_\_$ .

The angular speed $w$ of an object traveling around a circle of radius $r$ is the angle $\theta$ (measured in radians) swept out, divided by the elapsed time $t$ .

For circular motion on a circle of radius $r$, linear speed equals angular speed divided by $r$ .

Draw the angle in standard position.

$30°$

Draw the angle in standard position.

$60°$

Draw the angle in standard position.

$135°$

Draw the angle in standard position.

$-120°$

Draw the angle in standard position.

$450°$

 Draw the angle in standard position. 

$540°$

Draw the angle in standard position.

$\frac{3\pi }{4}$

Draw the angle in standard position.

$\frac{4\pi }{3}$

 Draw the angle in standard position. 

$\frac{-\pi }{6}$

Draw the angle in standard position.  

$\frac{-2\mathrm{\pi }}{3}$

Draw the angle in standard position.  

$\frac{16\mathrm{\pi }}{3}$

Draw the angle in standard position.  

$\frac{21\mathrm{\pi }}{3}$

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$40°10\text{'}25\text{'}\text{'}$

In Problems 23–28, convert each angle to a decimal in degrees. Round your answer to two decimal places.

$40°10\text{'}25\text{'}\text{'}.$

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$61°42\text{'}21\text{'}\text{'}$

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$1°2\text{'}3\text{'}\text{'}$

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$73°40\text{'}40\text{'}\text{'}$

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$9°9\text{'}9\text{'}\text{'}$

Convert each angle to a decimal in degrees. Round your answer to two decimal places.$98°22\text{'}45\text{'}\text{'}$

Convert each angle to DMS form. Round your answer to the nearest second.

$40.32°$

Convert each angle to DMS form. Round your answer to the nearest second.

$61.24°$

Convert each angle to DMS form. Round your answer to the nearest second.

$18.255°$

convert each angle to DMS form. Round your answer to the nearest second.

$29.411°$

Convert each angle to DMS form. Round your answer to the nearest second.

$19.99°$

Convert each angle to DMS form. Round your answer to the nearest second.

$44.01°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$30°$

Covert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$240°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$330°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$-60°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$-30°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$180°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$270°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$-135°$

Convert each angle in degree to radians. express your answer as a multiple of $\mathrm{\pi }$.

$-225°$

Convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

$-90°$

Convert each angle in degrees to radians. Express your answer  as a multiple of$\mathrm{\pi }$.

$-180°$