# How do you find a numerical value of one trigonometric function of x given tanx=1/4secx?

Nov 12, 2016

$x = 0.2526802551 + 2 \pi n \mathmr{and} x = 2.888912398 + 2 \pi n$

#### Explanation:

$\tan x = \frac{1}{4} \sec x$

$\sin \frac{x}{\cos} x = \frac{1}{4} \cdot \frac{1}{\cos} x$

$\sin \frac{x}{\cos} x \cdot \cos x = \frac{1}{4} \cdot \frac{1}{\cos} x \cdot \cos x$

$\sin \frac{x}{\cancel{\cos}} x \cdot \cancel{\cos} x = \frac{1}{4} \cdot \frac{1}{\cancel{\cos}} x \cdot \cancel{\cos} x$

$\sin x = \frac{1}{4}$

$x = {\sin}^{-} 1 \left(\frac{1}{4}\right)$

$x = 0.2526802551 + 2 \pi n \mathmr{and} x = \left(\pi - 0.2526802551\right) + 2 \pi n$

$x = 0.2526802551 + 2 \pi n \mathmr{and} x = 2.888912398 + 2 \pi n$