Question

How do you find the complement and supplement of $\dfrac{\pi }{3}$ ?

Answer 1

We have to find the complementary and supplementary angles of $\dfrac{\pi }{3}$. We will subtract $\dfrac{\pi }{3}$ from $\dfrac{\pi }{2}$ to find the complementary angle and subtract $\dfrac{\pi }{3}$from $\pi$ to find the supplementary angle. By solving the equations we get the desired answer.

Complete step by step solution:
We have been given a measure of angle $\dfrac{\pi }{3}$.
We have to find the complement and supplement of a given angle.
Now, we know that sum of two complementary angles is $\dfrac{\pi }{2}$ so to find the complement of the given angle we need to subtract $\dfrac{\pi }{3}$ from $\dfrac{\pi }{2}$. Then we will get
$\Rightarrow \dfrac{\pi }{2}-\dfrac{\pi }{3}$
Now, solving the above obtained equation we will get
$\begin{aligned} & \Rightarrow \dfrac{3\pi -2\pi }{6} \\\ & \Rightarrow \dfrac{\pi }{6} \\\ \end{aligned}$
Now, we know that the sum of two supplementary angles is $\pi$. So to find the supplement of the given angle we need to subtract $\dfrac{\pi }{3}$from $\pi$. Then we will get
$\Rightarrow \pi -\dfrac{\pi }{3}$
Now, solving the above obtained equation we will get
$\begin{aligned} & \Rightarrow \dfrac{3\pi -\pi }{3} \\\ & \Rightarrow \dfrac{2\pi }{3} \\\ \end{aligned}$
Hence we get the complement of $\dfrac{\pi }{3}$ as $\dfrac{\pi }{6}$ and supplement of $\dfrac{\pi }{3}$ as $\dfrac{2\pi }{3}$.

Note: Here in this question we have been given the measure of angle in radians so we use the values in radians to solve the question and get the answer also in radians. If we have given the measure of angles in degree then we use the values as the sum of two complementary angles is $90{}^\circ$ and sum of two supplementary angles is $180{}^\circ$.