Question

How do you find the value of $\csc 60^\circ $?

Answer 1

Hint: To find out the value of the above trigonometry function, we convert cosec into sin or cos function then we put the value of these functions from the trigonometric table and simplify these values by reciprocal the denominator.

Complete step by step solution:
As per the question, we need to find the value of $\csc 60^\circ $.
First of all we will convert cosec into sin function, the trigonometric function$\csc \theta = \dfrac{1}{{\sin \theta }}$
$ = \csc 60^\circ \Rightarrow \dfrac{1}{{\sin 60^\circ }}......(1)$
As per the trigonometric table $\sin 60^\circ = \dfrac{{\sqrt 3 }}{2}$ put this value in the above equation (1)
$ = \dfrac{1}{{\sin 60^\circ }} \Rightarrow \dfrac{1}{{\dfrac{{\sqrt 3 }}{2}}}$
We know that dividing by a number is the same as multiply by the same number, so we reciprocal the denominator as shown below:
$ = \dfrac{1}{1} \times \dfrac{2}{{\sqrt 3 }} \Rightarrow \dfrac{2}{{\sqrt 3 }}$

Hence, $\csc 60^\circ = \dfrac{2}{{\sqrt 3 }}$.

Note:
We should know that we always need to convert all trigonometry functions into $\sin \theta $ and $\cos \theta $. Also, we have to remember the values available in trigonometric tables so that we can use them directly in the questions to reduce work and save time.