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# How to find the value of $x$ where $0 \le x \le {360^ \circ }$ for $\sec x = - 1.7172$?

Last updated date: 10th Aug 2024
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Hint:
Here we will find the value of $x$ by using trigonometric function identity. First, we will convert the secant function into a cosine function by using the reciprocal trigonometric identity. Then we will find the value of $\cos x$. Finally, we will take cosine inverse to get the required answer.

Complete step by step solution:
We have to find the value of $x$ for $\sec x = - 1.7172$.
We know that secant is also defined as reciprocal of cosine function i.e. $\sec x = \dfrac{1}{{\cos x}}$.
Therefore, using this identity, we can write
$\sec x = \dfrac{1}{{\cos x}} = - 1.7172$
On cross multiplying the terms, we get
$\Rightarrow \cos x = \dfrac{1}{{ - 1.7172}}$
Dividing the terms, we get
$\Rightarrow \cos x = - 0.5823$
Now, taking the inverse cosine function on both the sides, we get
$\Rightarrow x = {\cos ^{ - 1}}\left( { - 0.5823} \right)$
Using the calculator we get,
$x = {125.61^ \circ }$

So, we get the value of $x$ as ${125.61^ \circ }$.