Trigonometry - Radians and Conversions

Change the following expression to degrees:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}$

$60^{\circ}$

$90^{\circ}$

$75^{\circ}$

$160^{\circ}$

$120^{\circ}$

Explanation

First we need to simplify the expression:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}=\frac{\frac{2\pi-\pi}{6}}{\frac{2+1}{6}}=\frac{\pi}{3}$

Now multiply by $\frac{180^{\circ}}{\pi}$ :

$\frac{\pi}{3}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{3}=60^{\circ}$

Convert $\pi$ into degrees.

$180^{\circ}$

$90^{\circ}$

$30^{\circ}$

$360^{\circ}$

$3.14^{\circ}$

Explanation

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$\pi*\frac{180}{\pi}=180^{\circ}$ .

Convert $\frac{2\pi}{5}$ to degrees:

$72^{\circ}$

$114^{\circ}$

$36^{\circ}$

$\frac{2}{5}^{\circ}$

$72\pi$

Explanation

To convert radians to degrees, we need to multiply the given radians by $\frac{180^{\circ}}{\pi}$ .

$\frac{2\pi}{5}*\frac{180^{\circ}}{\pi}=\frac{360^{\circ}}{5}=72^{\circ}$

Simplify and give the followoing expression in degrees:

$\frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}$

$450^{\circ}$

$420^{\circ}$

$480^{\circ}$

$350^{\circ}$

$380^{\circ}$

Explanation

First we need to simplify the expression:

$\frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}=\frac{\frac{4\pi+\pi}{14}}{\frac{1}{7}}=\frac{5\pi}{2}$

Then multiply by $\frac{180^{\circ}}{\pi}$ :

$\frac{5\pi}{2}\times \frac{180^{\circ}}{\pi}=\frac{5\times 180^{\circ}}{2}=450^{\circ}$

Convert $\frac{4\pi}{3}$ into degrees.

$240^{\circ}$

$200^{\circ}$

$100^{\circ}$

$250^{\circ}$

$248^{\circ}$

Explanation

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that, $360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$\frac{4\pi}{3}*\frac{180}{\pi}=240^{\circ}$ .

Convert one degree to radians.

$\frac{\pi}{180}$

$\frac{\pi}{90}$

$\frac{\pi}{120}$

$\frac{\pi}{60}$

$\pi$

Explanation

In order to change degrees to radians we need to multiply the degrees by $\frac{\pi}{180^{\circ}}$ :

$1^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{180}$

Convert $\frac{7\pi}{4}$ radians into degrees.

$315^{\circ}$

$270^{\circ}$

$345^{\circ}$

$285^{\circ}$

$225^{\circ}$

Explanation

Recall the definition of "radians" derived from the unit circle:

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

The quantity of radians given in the problem is $\frac{7\pi}{4}$ . All that is required to convert this measure into degrees is to denote the unknown angle measure in degrees by $\Theta$ and set up a proportion equation using the aforementioned definition relating radians to degrees: