Question

What is the equivalent degree measure for
`(3\pi)/(4)`radians?

Answer 1

Given:

`(3\pi)/(4)`

Required: Equivalent in degree

Solution:

Let the equivalent of

`(3\pi)/(4)`

be represented as X.

Thus,

`(3\pi)/(4)\text{ = X}`

But

`\pi radians=180^(\circ)`

This implies that

`\begin{gathered} \pi=180^(\circ) \\ (3\pi)/(4)\text{ = X} \end{gathered}`

By cross-multiplication, we have

`\begin{gathered} \pi\text{ }*\text{ X = 180 }*\text{ }(3\pi)/(4) \\ X\pi\text{ = }(180*3\pi)/(4) \end{gathered}`

Divide both sides by the coefficient of X.

The coefficient of X is π.

Thus,

`\begin{gathered} X\text{ = }(180*3\pi)/(4)*(1)/(\pi) \\ \Rightarrow X\text{ = 135} \end{gathered}`

Hence, the equivalent of

`(3\pi)/(4)\text{ radians}`

is 135°