Question

How do you find the complement and supplement of 1 radians?

Answer 1

Hint: Two angles are said to be complement if the sum of two angles is 90 degrees. Two angles are said to be supplemented if the sum of two angles is 180 degrees. The value of 1 radian is 57.2958 degrees. The value of 1 degree is 0.0174533 radians.

Complete step by step answer:
As per the given question, we are given 1 radian and we need to find the complement and supplement of 1 radians.
Complement of 1 radian :
Let us assume x be the complement of 1 radian then the sum of 1 radian and x will be equal to 90 degrees.
\[\Rightarrow x+1=\dfrac{\pi }{2}\]
Now we add -1 on both sides
\[\begin{align}
  & \Rightarrow x+1-1=\dfrac{\pi }{2}-1 \\
 & \Rightarrow x=\dfrac{\pi }{2}-1 \\
\end{align}\]
\[\Rightarrow x=0.5708radian\]
Therefore, the complement of 1 radian is \[0.5708\] radian.
supplement of 1 radian :
Let us assume y be the complement of 1 radian then the sum of 1 radian and x will be equal to 180 degrees.
\[\Rightarrow y+1=\pi \]
Now we add -1 on both sides
\[\begin{align}
  & \Rightarrow y+1-1=\pi -1 \\
 & \Rightarrow y=\pi -1 \\
\end{align}\]
\[\Rightarrow y=2.1416radian\]
Therefore, the supplement of 1 radian is \[2.1416\]radian.

Therefore, the complement of 1 radian is \[0.5708\] radian and the supplement of 1 radian is \[2.1416\]radian.

Note: In order to solve such types of questions, we need to have enough knowledge over the values of radians and degrees. We can also find the value of supplement and complement in degrees. We also need to know the algebraic formulae to simplify the expressions. We must avoid calculation mistakes to get the expected answers.