Question

What is the value of \[\cos \left( \dfrac{2\pi }{3} \right)\]?

Answer 1

Hint: In the above type of question we need to first check the angle that has been mentioned and also in which form it is. We should know how we can convert radians into degrees as we know the cosine values in which angles are in degree.

Complete step by step solution:
In the above type of question we should first check the value of angle and in which form it is written if it is given in radians we need to convert it into degrees to solve the question easier and in a faster manner.
In the above mentioned question the given value is in radians as the value of \[\pi \] is 3.14 so this will give the angle in radians but to convert it in degrees we will use the value of \[\pi \]as 180 then the value received in the end will give us the angle in degrees, so when we substitute the value of \[\pi \] as 180 in our given question we will get it as
\[\begin{align}
  & =\cos \left( \dfrac{2\left( 180 \right)}{3} \right) \\
 & =\cos \left( 120 \right) \\
\end{align}\]
Now we can see that we got the angle more than 90 so in the 2nd quarter i.e. if the angle is in between 90 and 180 we will subtract the value by 90 and find the cosine value of the resultant angle i.e.
\[\begin{align}
  & \cos \left( 120 \right)=-\cos \left( 120-90 \right) \\
 & =-\cos \left( 30 \right) \\
\end{align}\]
This is a property of cosine, so that we can find the values of cosine whose angles are between 90 to 180 with ease and faster way. Now the value of the value mentioned in the question came out to be \[-\cos \left( 30 \right)=-\dfrac{1}{2}\].

So the final value of \[\cos \left( \dfrac{2\pi }{3} \right)\] is \[-\dfrac{1}{2}\].

Note: In the above type of question there is general mistakes that happen that we change the value of the angle as per the rules but forget to write the sign in front of it i.e. positive or negative so to not forget remember in which quarter what is the sign of cosine, tan, sine so that when taking out values you can correctly solve them.