The Unit Circle and Radians

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Math › The Unit Circle and Radians

Questions 1 - 10

How many radians are in $270^\circ$ ?

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

$2\pi$

$\pi$

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

$\frac{5\pi}{2}$

Explanation

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{270^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$270^\circ*\pi=180^\circ*x$

Isolate :

$\frac{270^\circ}{180^\circ}\pi=x$

$\frac{3\pi}{2}=x$

How many radians are in $270^\circ$ ?

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

$2\pi$

$\pi$

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

$\frac{5\pi}{2}$

Explanation

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{270^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$270^\circ*\pi=180^\circ*x$

Isolate :

$\frac{270^\circ}{180^\circ}\pi=x$

$\frac{3\pi}{2}=x$

If Angle equals $72^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

$1.26\ radians$

$4125.29\ radians$

$4.125\ radians$

$1256.6\ radians$

$0.628\ radians$

Explanation

To convert between radians and degrees, it is important to remember that:

$\pi, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$72^{\circ}\cdot \frac{\pi}{180^{\circ}} = 1.26,rad$

If Angle equals $72^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

$1.26\ radians$

$4125.29\ radians$

$4.125\ radians$

$1256.6\ radians$

$0.628\ radians$

Explanation

To convert between radians and degrees, it is important to remember that:

$\pi, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$72^{\circ}\cdot \frac{\pi}{180^{\circ}} = 1.26,rad$

What is the value of the angle $\frac{3\pi}{2}$ radians when converted to degrees?

Explanation

The answer can be found using the conversion of 1 radian equals $\frac{180}{\pi}$ degrees. Multiplying $\frac{3\pi}{2}$ by this conversion factor gives 270 degrees.

What is the value of the angle $\frac{3\pi}{2}$ radians when converted to degrees?

Explanation

The answer can be found using the conversion of 1 radian equals $\frac{180}{\pi}$ degrees. Multiplying $\frac{3\pi}{2}$ by this conversion factor gives 270 degrees.

A point has Cartesian coordinates . Rewrite this as an ordered pair in the polar coordinate plane, rounding the coordinates to the nearest hundredth.