Question

If angle X is an acute angle with tan X = 8/7, what is the value of sec X?

Answer 1

Answer: $\frac{\sqrt{113}}{7}$

Step-by-step explanation:

As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.

Using the identity $1+\tan^{2} X=\sec^{2} X$,

$1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}$