Find the exact value of the trigonometric function sec ((-9pi)/4) .

Find the exact value of the trigonometric function sec ((-9pi)/4) .

Question
Trigonometric Functions
asked 2020-11-26
Find the exact value of the trigonometric function \(\displaystyle{\sec{{\left(\frac{{-{9}\pi}}{{4}}\right)}}}\) .

Answers (1)

2020-11-27
We know that
\(\displaystyle{\sec{{\left(-{x}\right)}}}={\sec{{\left({x}\right)}}}\)
Therefore,
\(\displaystyle{\sec{{\left(\frac{{-{9}\pi}}{{4}}\right)}}}={\sec{{\left(\frac{{{9}\pi}}{{4}}\right)}}}\)
Rewriting the above trigonometric function,
\(\displaystyle{\sec{{\left(\frac{{{9}\pi}}{{4}}\right)}}}={\sec{{\left(\frac{{{8}\pi+\pi}}{{4}}\right)}}}\)
\(\displaystyle={\sec{{\left(\frac{{{8}\pi}}{{4}}+\frac{\pi}{{4}}\right)}}}\)
\(\displaystyle={\sec{{\left({2}\pi+\frac{\pi}{{4}}\right)}}}\)
We know that \(\displaystyle{2}\pi+\theta\) lies in first quadrant and in first quadrant all trigonometric functions are positive.
Therefore,
\(\displaystyle{\sec{{\left({2}\pi+\frac{\pi}{{4}}\right)}}}={\sec{{\left(\frac{\pi}{{4}}\right)}}}\)
\(\displaystyle=\sqrt{{2}}\)
Hence, exact value of given trigonometric function is \(\displaystyle\sqrt{{2}}\)
0

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