Radians and Conversions - Trigonometry

Card 1 of 204

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

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

Tap to reveal answer

Answer

In order to change an angle into degrees, you must multiply the radian by .

Therefore, to solve:

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

← Didn't Know|Knew It →

Question

Change $\frac{\pi}{5}$ angle to degrees.

Tap to reveal answer

Answer

In order to change radians to degrees, we need to multiply the radian agle measure by .

$\frac{\pi}{5}$\times $$\frac{180^{\circ}$$$}{\pi}=\frac{180^{\circ}$$$}{5}=36^{\circ}$

← Didn't Know|Knew It →

Question

An angle of 40 radians is equal to how many degrees?

Tap to reveal answer

Answer

We know that one radian is equal to , so in order to change radians to degrees we need to multiply by .

$40\times $$\frac{180^{\circ}$$$}{\pi}=\frac{7200^{\circ}$$}{\pi}$

← Didn't Know|Knew It →

Question

Change $\frac{17\pi}{5}$ angle to degrees.

Tap to reveal answer

Answer

In order to change radians to degrees we need to multiply the radians by .

$\frac{17\pi}{5}$\times $$\frac{180^{\circ}$$}{\pi}=\frac{17\times $180^{\circ}$$$}{5}=612^{\circ}$

← Didn't Know|Knew It →

Question

Change to radians.

Tap to reveal answer

Answer

In order to change degrees to radians we need to multiply the degrees by .

← Didn't Know|Knew It →

Question

Change the following expression to degrees:

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

Tap to reveal answer

Answer

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 :

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

← Didn't Know|Knew It →

Question

Change the following expression to degrees:

${$\frac{\pi}{4}$-$\frac{\pi}{12}$}$

Tap to reveal answer

Answer

First we need to simplify the expression:

${$\frac{\pi}{4}$-$\frac{\pi}{12}$}=\frac{3\pi-\pi}{12}$=\frac{2\pi}{12}$=\frac{\pi}{6}$$

Then multiply the radians by :

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

← Didn't Know|Knew It →

Question

Convert the following expression to radians:

Tap to reveal answer

Answer

First we need to simplify the expression:

In order to change degrees to radians, we need to multiply by :

← Didn't Know|Knew It →

Question

Change to radians.

Tap to reveal answer

Answer

In order to change degrees to radians we need to multiply degrees by :

← Didn't Know|Knew It →

Question

Convert one radian to degrees.

Tap to reveal answer

Answer

In order to change radians to degrees we need to multiply radians by :

$1\times $$\frac{180^{\circ}$$$}{\pi}=\frac{180^{\circ}$$}{\pi}\approx $57.3^{\circ}$$

← Didn't Know|Knew It →

Question

Convert one degree to radians.

Tap to reveal answer

Answer

In order to change degrees to radians we need to multiply the degrees by :

← Didn't Know|Knew It →

Question

Simplify and give the followoing expression in degrees:

$2\pi-$\frac{\pi}{4}$$

Tap to reveal answer

Answer

First we need to simplify the expression:

$2\pi-$\frac{\pi}{4}$=\frac{8\pi-\pi}{4}$=\frac{7\pi}{4}$$

Then multiply by :

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

← Didn't Know|Knew It →

Question

Simplify and give the followoing expression in degrees:

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

Tap to reveal answer

Answer

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 :

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

← Didn't Know|Knew It →

Question

Give in radians:

Tap to reveal answer

Answer

First we need to convert degrees to radians by multiplying by :

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}$$

← Didn't Know|Knew It →

Question

Give in radians:

Tap to reveal answer

Answer

First we need to convert degrees to radians by multiplying by :

Now we can write:

← Didn't Know|Knew It →

Question

Give in degrees:

$$\frac{3x+6\pi}{2}$=4\pi$

Tap to reveal answer

Answer

First we can find in radians:

$$\frac{3x+6\pi}{2}$=4\pi\Rightarrow 3x+6\pi=2\times 4\pi$

$\Rightarrow 3x+6\pi=8\pi\Rightarrow 3x=8\pi-6\pi$

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

To change radians to degrees we need to multiply radians by . So we can write:

$x=\frac{2\pi}{3}$\Rightarrow x=\frac{2\pi}{3}$\times $$\frac{180^{\circ}$$$}{\pi}=120^{\circ}$$

← Didn't Know|Knew It →

Question

Give in degrees:

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

Tap to reveal answer

Answer

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 . So we can write:

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

← Didn't Know|Knew It →

Question

Give in radians:

Tap to reveal answer

Answer

First we need to convert to radians by multiplying by :

Now we can solve the following equation for :

$\Rightarrow {$\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}$$

← Didn't Know|Knew It →

Question

Give in degrees:

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

Tap to reveal answer

Answer

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 . So we can write:

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

← Didn't Know|Knew It →

Question

Convert the angle $\frac{7\pi }{3}$ into degrees.

Tap to reveal answer

Answer

To convert radians to degrees, use the conversion .

In this case:

$($\frac{7\pi $}{3}$)*($\frac{180^{\circ}$$}{\pi }) = $420^{\circ}$$

← Didn't Know|Knew It →

0

Knew It