Question

Evaluate: sec(5 pie/4)

Answer 1

Answer:

$sec(\frac{5\pi}{4})=-\sqrt{2}$

Step-by-step explanation:

$sec(\frac{5\pi}{4})\\\\=\frac{1}{cos(\frac{5\pi}{4})}\\ \\=\frac{1}{-\frac{\sqrt{2}}{2}}\\ \\=-\frac{2}{\sqrt{2}}\\ \\=-\frac{2\sqrt{2}}{2}\\ \\=-\sqrt{2}$

It really helps to use the unit circle for solving these kinds of problems. I've attached one for your convenience. Note that a point on the unit circle, given the angle in radians, is defined as $(cos\theta,sin\theta)$.