How to find quadrant of triangle in this problem?

Question

The problem is tan(arcsec(-7)). I know I must draw the triangle of arcsec(-7) and find the tangent from there, but I can't remember how to find out which quadrant to draw the triangle in. I know secant is negative which means cosine must be negative, which means either quadrants 3 or 2, but which of the two do i choose??

Answer 1

Here are the quadrants for all of the inverse trig functions:

Arcsin, ArcCSC, and Arctan - Q1 and Q2

Arccos, Arcsec, and ArcCot - Q1 and Q4.

You never choose quadrant 3.