Question

Evaluate: sec(5 pie/4)

Answer 1

`sec((5\pi)/(4))=-√(2)`

Explanation:

`sec((5\pi)/(4))\\\\=(1)/(cos((5\pi)/(4)))\\ \\=(1)/(-(√(2))/(2))\\ \\=-(2)/(√(2))\\ \\=-(2√(2))/(2)\\ \\=-√(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)`.