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# How to find the value of $\csc 10$?

Last updated date: 23rd Jul 2024
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Hint:
Here we will find the value of the given trigonometric function. First, we will convert the given trigonometric function into sine function by using the reciprocal trigonometric identity. Then we will use the calculator to find the value of obtained sine function. Then we will simplify the equation further to get the required answer.

Complete step by step solution:
We have to find the value of $\csc 10$.
We know that cosecant is also define as reciprocal sine function i.e. $\csc x = \dfrac{1}{{\sin x}}$.
Therefore, we will convert the given cosecant function in sine function as,
$\csc 10 = \dfrac{1}{{\sin 10}}$…..$\left( 1 \right)$
Next, we will use calculator and find the value of $\sin 10$ and substitute it in above equation. Therefore, we get
$\Rightarrow \csc 10 = \dfrac{1}{{ - 0.54402}}$
Dividing the terms, we get
$\Rightarrow \csc 10 = - 1.838$

So we get the value of $\csc 10$ as $- 1.838$.