Question

How do you convert $\dfrac{15\pi }{4}$ into degree?

Answer 1

Hint: In this question, we have to convert a radian into a degree. In trigonometric, the angle can be measured in two forms, either in degrees or in a radian. A radian is a measure of an angle; it is the ratio of the length of the arc to the radius of the circle. If it is given to us a degree, we can convert it into radian or vice-versa. Thus, to solve this problem, we use the degree-radian conversion formula. We start solving this problem, by using the formula $1\text{ }radian=\dfrac{{{180}^{\circ }}}{\pi }$ . We multiply both sides of the equation by $15\pi $ , and then divide $4$ on both sides of the equation. Then, we make further calculations in the RHS of the equation, to get the required solution, which is in the form of degrees.

Complete answer:
According to the question, we have to convert a radian angle into a degree angle.
The angle given to us is $\dfrac{15\pi }{4}$ radian -------- (1)
Now, to convert it into degree angle,
We will use the degree-radian conversion formula, $1\text{ }radian=\dfrac{{{180}^{\circ }}}{\pi }$ ------------ (2)
So, now we will multiply $15\pi $ on both sides in the equation (2), we get
$\Rightarrow 15\pi \text{ }radian=\dfrac{{{180}^{\circ }}}{\pi }.(15\pi )$
Now, divide both sides of the equation by $4$ , therefore we get
$\Rightarrow \dfrac{15\pi }{4}\text{ }radian=\dfrac{{{180}^{\circ }}}{\pi }.(15\pi ).\dfrac{1}{4}$
Now, we will cancel both the $\pi $ on the RHS of the above equation, to get
 $\Rightarrow \dfrac{15\pi }{4}\text{ }radian={{180}^{\circ }}.(15).\dfrac{1}{4}$
On further simplification, we get
$\Rightarrow \dfrac{15\pi }{4}\text{ }radian={{45}^{\circ }}.(15)$
In the last, we multiply both the numbers on the RHS, we get
$\Rightarrow \dfrac{15\pi }{4}\text{ }radian={{675}^{\circ }}$
Therefore, we get the conversion of radian into degrees. The angle given to us is $\dfrac{15\pi }{4}$ , after converting it into a degree, we get ${{675}^{\circ }}\text{degree}$ , which is our required solution.

Note: In radian-degree conversions, always mention the units in each step that helps us to understand which side is the degree and which side is the radian of an equation. If in the question, we have to convert the degree into radian, then we will use the formula ${{1}^{\circ }}=\dfrac{\pi }{180}\text{ radian}$ .