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Question: How do you convert \(\dfrac{15\pi }{4}\) into degree?...

How do you convert 15π4\dfrac{15\pi }{4} into degree?

Explanation

Solution

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 radian=180∘π1\text{ }radian=\dfrac{{{180}^{\circ }}}{\pi } . We multiply both sides of the equation by 15π15\pi , and then divide 44 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 15π4\dfrac{15\pi }{4} radian -------- (1)
Now, to convert it into degree angle,
We will use the degree-radian conversion formula, 1 radian=180∘π1\text{ }radian=\dfrac{{{180}^{\circ }}}{\pi } ------------ (2)
So, now we will multiply 15π15\pi on both sides in the equation (2), we get
⇒15π radian=180∘π.(15π)\Rightarrow 15\pi \text{ }radian=\dfrac{{{180}^{\circ }}}{\pi }.(15\pi )
Now, divide both sides of the equation by 44 , therefore we get
⇒15π4 radian=180∘π.(15π).14\Rightarrow \dfrac{15\pi }{4}\text{ }radian=\dfrac{{{180}^{\circ }}}{\pi }.(15\pi ).\dfrac{1}{4}
Now, we will cancel both the π\pi on the RHS of the above equation, to get
⇒15π4 radian=180∘.(15).14\Rightarrow \dfrac{15\pi }{4}\text{ }radian={{180}^{\circ }}.(15).\dfrac{1}{4}
On further simplification, we get
⇒15π4 radian=45∘.(15)\Rightarrow \dfrac{15\pi }{4}\text{ }radian={{45}^{\circ }}.(15)
In the last, we multiply both the numbers on the RHS, we get
⇒15π4 radian=675∘\Rightarrow \dfrac{15\pi }{4}\text{ }radian={{675}^{\circ }}
Therefore, we get the conversion of radian into degrees. The angle given to us is 15π4\dfrac{15\pi }{4} , after converting it into a degree, we get 675∘degree{{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∘=π180 radian{{1}^{\circ }}=\dfrac{\pi }{180}\text{ radian} .