Hwk 1 – Angles

Convert the angle ${240}^{\circ }$ to radians. Give the exact value and use pi for $\pi$.

Convert the angle $\frac{5\pi }{6}$ from radians to degrees.

 degrees

Convert the angle $\frac{5\pi }{6}$ from radians to degrees.

 degrees

Convert the angle ${240}^{\circ }$ to radians. Give the exact value and use pi for $\pi$.

Convert 190 degrees to radians

    radians

Convert $\frac{\pi }{9}$ to degrees

    degrees

Give a exact answers, using pi for $\pi$ if needed

Convert the angle $\frac{11\pi }{6}$ from radians to degrees:

$\frac{11\pi }{6}=$  °

Convert the following angle from decimal form to degrees-minutes-seconds (DMS) form:

${118.5625}^{\circ }=$ ° $‘$ $‘‘$

Convert the following angle from degrees-minutes-seconds (DMS) form to decimal form:

${140}^{\circ }50‘42‘‘$ = °

Convert the angle from its decimal representation to Degrees-Minutes-Seconds representation:

${139.732}^{\circ }$=° $‘$ $‘‘$

Convert the angle from its Degrees-Minutes-Seconds representation to decimal representation:

${29}^{\circ }18‘44‘‘$ = 

The angle between $0^{\circ }$ and ${360}^{\circ }$ that is coterminal with the ${1174}^{\circ }$ angle is     degrees.

The angle between $0^{\circ }$ and ${360}^{\circ }$ that is coterminal with the $-{788}^{\circ }$ angle is     degrees.

Find an angle between 0° and 360° that is coterminal with the given angle.

$566°$ is coterminal to °
$-91°$ is coterminal to °
$-1612°$ is coterminal to °
$9838°$ is coterminal to °

Write an expression describing all the angles that are coterminal with 93°. (Please use the variable $k$ in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)

 degrees   

Given an angle with measure $\frac{-\pi }{4}$ find the following.

Find a coterminal angle between $-4\pi$ and $-2\pi$.    

Find a coterminal angle between $0$ and $2\pi$.    

The angle between 0 and $2\pi$ in radians that is coterminal with the angle $-\frac{23\pi }{4}$ radians is     .

In a circle of radius 4 miles, the length of the arc that subtends a central angle of 5 radians is     miles.

Find the distance along an arc on the surface of the earth that subtends a central angle of 6 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)
Your answer is     miles.

On a circle of radius 9 feet, what angle would subtend an arc of length 4 feet?

    degrees

Find the length of the arc subtended by the angle $8^{\circ }42‘$ with a radius of 18.6.   Give your answer rounded to 4 decimal places.

If a an arc of length 20.4 furlongs subtends a central angle of 5.1 radians on a circle, then the radius of the circle has length:

 furlongs

A circular arc of length 6 feet subtends a central angle of 85 degrees. Find the radius of the circle in feet. (Note: You can enter $\pi$ as ‘pi’ in your answer.)
    feet

Find the distance that the earth travels in one day in its path around the sun. Assume that a year has 365 days and that the path of the earth around the sun is a circle of radius 93 million miles.
Your answer is     million miles.

Find the area of the sector of a circle with radius 10 miles formed by a central angle of 245°:

 square miles

Round your answer to two decimal places.

Find the area of the sector of a circle with radius 6 yards formed by a central angle of $\pi$  radians. Give your answer in terms of pi.

    square yards

Find the area of the sector of a circle with radius 5 meters formed by a central angle of $\frac{4\pi }{3}$  radians. Give your answer correct to 3 decimal places

 square meters

Find the area of the sector of a circle with radius 12 feet formed by a central angle of 215°:

 square feet

Round your answer to two decimal places.

A saw uses a circular blade 8 inches in diameter that spins at 3160 rpm. How quickly are the teeth of the saw blade moving? Express your answer in several forms:

In exact feet per second:     ft/sec

In approximate feet per second, rounded to 1 decimal place:  ft/sec

In exact miles per hour:     mph

In approximate miles per hour, rounded to 1 decimal place:  mph

A truck’s 30-in.-diameter wheels are turning at 575 rpm.

Find the linear speed of the truck in mph:

    miles/hour

Write answer as an exact expression using pi for $\pi$. No need to simplify.

A truck with 20-in.-diameter wheels is traveling at 45 mi/h.

Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes:     rad/min

How many revolutions per minute do the wheels make?     rpm

Round your answers to 1 decimal place.