SAT Math - Radians | Practice Hub

How many radians are in $300^\circ$ ?

$\frac{5\pi}{3}$

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

$\frac{3\pi}{5}$

$\frac{7\pi}{3}$

$\pi\sqrt{3}$

Explanation

Since $180^\circ=\pi\ \text{radians}$ , we can solve by setting up a proportion:

$\frac{300^\circ}{x}=\frac{180^\circ}{\pi}$

Cross-multiply and solve.

$300^\circ*\pi=180^\circ*x$

$\frac{300^\circ}{180^\circ}\pi=x$

$\frac{5\pi}{3}=x$

Convert $\frac{11\pi}{5}$ into degrees.

$396\degree$

$400\degree$

$395\degree$

$300\degree$

Explanation

To convert from radians to degrees, you must multiply the angle by $\frac{180\degree}{\pi}$ to cancel the $\pi$ units.

This will get you

$11\cdot \frac{180\degree}{5}=396^\circ$

Convert $1^{\circ}$ into radians.

$\frac{\pi}{180}$

$\frac{\pi}{360}$

$\pi$

$2\pi$

$\frac{\pi}{90}$

Explanation

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

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

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$1*\frac{\pi}{180}=\frac{\pi}{180}$ .

Give in radians:

$\frac{72^{\circ}-\pi}{2x-\pi}=3$

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

$x=\frac{4\pi}{5}$

$x=\frac{3\pi}{5}$

$x=\frac{\pi}{5}$

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

Explanation

First we need to convert $72^{\circ}$ to radians by multiplying by $\frac{\pi}{180^{\circ}}$ :

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

Now we can solve the following equation for :

$\frac{72^{\circ}-\pi}{2x-\pi}=3\Rightarrow \frac{\frac{2\pi}{5}-\pi}{2x-\pi}=3$

$\Rightarrow {\frac{2\pi}{5}-\pi}=3(2x-\pi)\Rightarrow \frac{2\pi-5\pi}{5}=6x-3\pi$

$\Rightarrow -3\pi=30x-15\pi\Rightarrow 30x=12\pi$

$\Rightarrow x=\frac{12\pi}{30}\Rightarrow x=\frac{2\pi}{5}$

Change $\frac{4\pi }{3}$ angle to degrees.

$240^{\circ}$

$180^{\circ}$

$300^{\circ}$

$150^{\circ}$

Explanation

In order to change an angle into degrees, you must multiply the radian by $\frac{180^{\circ}}{\pi}$ .

Therefore, to solve:

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

Convert $\frac{\pi}{2}$ into degrees.

$90^\circ$

$180^\circ$

$60^\circ$

$55^\circ$

$30^\circ$

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,

$\frac{\pi}{2}*\frac{180}{\pi}=90^\circ$ .

Give in degrees:

$\frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}$

$x=30^{\circ}$

$x=36^{\circ}$

$x=40^{\circ}$

$x=60^{\circ}$

$x=90^{\circ}$

Explanation

First we can find in radians:

$\frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}\Rightarrow 2(\frac{\pi}{2}-x)=1(\frac{\pi}{2}+x)$

$\Rightarrow \pi-2x=\frac{\pi}{2}+x\Rightarrow \pi-\frac{\pi}{2}=3x$

$\Rightarrow 3x=\frac{\pi}{2}\Rightarrow x=\frac{\pi}{6}$

To change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ . So we can write:

$x=\frac{\pi}{6}\Rightarrow x=\frac{\pi}{6}\times \frac{180^{\circ}}{\pi}=30^{\circ}$

How many degrees is 3 radians?

$172^{\circ}$

$156^{\circ}$

$189^{\circ}$

$150^{\circ}$

None of these other answers.

Explanation

When going from radians to degrees one multiplies by the conversion factor

$\frac{180^{\circ}}{\pi rad}$ .

The radians cancel and the answer is left in degrees.

$3\hspace{1mm}{\color{Red} rad}\cdot\frac{180^{\circ}}{\pi {\color{Red} rad}}=\frac{540^\circ}{\pi}=172^{\circ}$

Give in degrees:

$\frac{4x-\pi}{2}=3\pi$

$x=315^{\circ}$

$x=345^{\circ}$

$x=305^{\circ}$

$x=300^{\circ}$

$x=415^{\circ}$

Explanation

First we can find in radians:

$\frac{4x-\pi}{2}=3\pi\Rightarrow 4x-\pi=2\times 3\pi$

$\Rightarrow 4x-\pi=6\pi\Rightarrow 4x=6\pi+\pi$

$\Rightarrow 4x=7\pi\Rightarrow x=\frac{7\pi}{4}$

To change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ . So we can write:

$x=\frac{7\pi}{4}\Rightarrow x=\frac{7\pi}{4}\times \frac{180^{\circ}}{\pi}=315^{\circ}$

Give in radians:

$\frac{x+\pi}{x-\pi}=30^{\circ}$

$x=\frac{\pi(\pi+6)}{\pi-6}$

$x=\frac{\pi+6}{\pi-6}$

$x=\frac{\pi(\pi+8)}{\pi-8}$

$x=\frac{\pi(\pi-6)}{\pi+6}$

$x=\pi$

Explanation

First we need to convert degrees to radians by multiplying by $\frac{\pi}{180^{\circ}}$ :

$30^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{6}$

Now we can write:

$\frac{x+\pi}{x-\pi}=\frac{\pi}{6}\Rightarrow 6(x+\pi)=\pi(x-\pi)$

$\Rightarrow 6x+6\pi=x\pi-\pi^2\Rightarrow 6x-x\pi=-6\pi-\pi^2$

$\Rightarrow x(6-\pi)=-\pi(\pi+6)$

$\Rightarrow x=\frac{-\pi(\pi+6)}{6-\pi}=\frac{\pi(\pi+6)}{\pi-6}$

Radians

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation