Question

How do you convert $270$ degrees to radians?

Answer 1

To convert degree to radians we have a formula, which is given by: $x\deg ree = \dfrac{\pi }{{180}}x\, radians$. Now in place of $x$ substitute the value in terms of degree they have given and solve for the correct answer. That is by simply multiplying the degree they have given with $\dfrac{\pi }{{180}}$ you will get the required answer in terms of radians.

Complete step-by-step answer:
In the question they have given in terms of degree, that is $270$ degrees.
They have asked to find the $270$ degrees in terms of radians.
So to convert degree to radians we have a relation between degree and radians given by:
$x\deg ree = \dfrac{\pi }{{180}}x\,radians$
By using the above relation we need to find the required answer.
From the above relation it is clear that one degree is equal to $\dfrac{\pi }{{180}}$ radians , that is if we substitute one in place of $x$ in relation equation.
Now, to calculate $270$ degrees in terms of radians, just multiply $270$ with $\dfrac{\pi }{{180}}$ to arrive at the required answer.
Therefore, we can write as
${270^ \circ } = 270 \times \dfrac{\pi }{{180}}radians$
Both $180$ and $270$ are divisible by $90$ so on simplification, we get
${270^ \circ } = \dfrac{{3\pi }}{2}radians$
Therefore, the $270$ degrees can be written as $\dfrac{{3\pi }}{2}$ radians.

Note: In this conversion type problem one thing we need to remember is conversion formula. If we feel like this is a lengthy process whenever they ask to convert the degree to radian, directly divide the value given in terms of degree by $180$ and reduce that to its lowest terms. Then finally multiply the answer or the result you got by $\pi$ we will get the same answer.