Question

How do you convert $\dfrac{{43\pi }}{{18}}$ into degrees?

Answer 1

Hint: Given a measure of an angle in radians. We have to find the measure of angle in degrees. First, we will multiply the expression by $\dfrac{{180^\circ }}{\pi }$. Then, we will simplify the expression. Then, if the measure of an angle is greater than $360^\circ $, then subtract the angle $360^\circ $ from the simplified angle in degrees.

Complete step-by-step answer:
We are given the measure of an angle in radians $\dfrac{{43\pi }}{{18}}$.

First, we will multiply the expression by $\dfrac{{180^\circ }}{\pi }$.

$ \Rightarrow \dfrac{{43\pi }}{{18}} = \dfrac{{43\pi }}{{18}} \times \dfrac{{180^\circ }}{\pi }$

On simplifying the expression, we get:

\[ \Rightarrow \dfrac{{43{\pi }}}{{{{18}}}} \times \dfrac{{{{180^\circ }}}}{{{\pi }}}\]

$ \Rightarrow 43 \times 10^\circ $

$ \Rightarrow 430^\circ $

Now, the angle is greater than $360^\circ $. So, we will determine the similar angle by subtracting $360^\circ $ from the angle $430^\circ $.

$ \Rightarrow 430^\circ - 360^\circ $

On simplifying the expression, we get:

$ \Rightarrow 70^\circ $


Final answer: Hence, the value of $\dfrac{{43\pi }}{{18}}$ in degrees is $70^\circ $

Additional information: The measure of an angle is represented in terms of radians or degrees. In degrees one complete rotation is equal to $360^\circ $ and in radians it is equal to $2\pi $. The concept of the degrees and radians are opposite to each other. The similar angle or coterminal angle is the angle which is obtained by subtracting $360^\circ $ from each angle if it is greater than $360^\circ $. The measure of angle in radians but lie between zero and $2\pi $. On the other hand, the angle in degrees must lie between $0^\circ $and $360^\circ $

Note:
In such types of questions the students mainly don't get an approach on how to solve it. In such types of questions students mainly forget to multiply the given expression by $\dfrac{{180^\circ }}{\pi }$. Then, students also forget to find the coterminal angle by subtracting the value of the complete circle from the computed value.