Question

How do you convert -150 degrees to radians?

Answer 1

Hint: In this problem, we have to convert the given degrees to its equivalent radians. We know that to convert the value of angle in degrees to its equivalent radians we should multiply the given value with $${\displaystyle \frac{\pi }{{180}^{\circ }}}$$ as the value of 180 degrees is $$\pi$$ in radians.

Complete step by step answer:
We know that the given degree is -150.
We should convert the given degrees to its equivalent radians.
We should know that, one complete revolution counter clockwise in an XY plane will be equal to $$2\pi$$(in radians) or 360 (in degrees), so we can write
$$\begin{array}{rl}& 2\pi ={360}^{\circ }\\ & \pi ={180}^{\circ }\end{array}$$
 We can see that $$\pi ={180}^{\circ }$$ and if we want to convert the value of angle in degrees to its equivalent radians, we should multiply the given value with $${\displaystyle \frac{\pi }{{180}^{\circ }}}$$.
We can multiply the given -150 value with $${\displaystyle \frac{\pi }{{180}^{\circ }}}$$, we get
$$\Rightarrow -150\times {\displaystyle \frac{\pi }{{180}^{\circ }}}$$
We can either take $$\pi$$ as 3.14 or we can use calculator to simplify the above step for the exact value, we get
$$\Rightarrow -150\times {\displaystyle \frac{\pi }{{180}^{\circ }}}={\displaystyle \frac{-5\pi }{6}}=-2.618$$radians.

Note: We should always remember the formula to convert from degree to radians or from radians to degrees to solve these types of problems. We should know that why we multiply the given number with $${\displaystyle \frac{\pi }{{180}^{\circ }}}$$ to convert into its radians as the value of 180 degrees is $$\pi$$ in radians. We should also concentrate on the multiplication part as we can take $$\pi$$ as 3.14 or $${\displaystyle \frac{22}{7}}$$ either we can use calculators.