Answer:
[tex]-\frac{\sqrt{21}}{2}[/tex]
Step-by-step explanation:
ASTC (I use a sentence to memorize: All Students Take Calculus):
Q1 - All functions are positive
Q2 - Sine is positive (Cosecant is positive as well) (all others negative)
Q3 - Tangent is positive (Cotangent is positive as well) (all others negative)
Q4 - Cosine is positive (Secant is positive as well) (all others negative)
Applying ASTC:
Secant is negative, so it can't be in quadrant 1, and quadrant 4.
Quadrant 2 - Sine and Quadrant 3 - Tangent are left.
Cosecant is positive so it can't be in quadrant 3.
Therefore, angle x is in Quadrant 2 or QII
Secant is hypotenuse / adjacent
5 = hypotenuse (hypotenuse is never a negative number)
-2 = adjacent
use pythagorean theorem to solve for opposite (bc tan = opp / adj)
[tex](-2)^2+o^2=5^2;4+o^2=25;o^2=21;o=\sqrt{21}[/tex]
tanx = [tex]\frac{\sqrt{21}}{-2}=-\frac{\sqrt{21}}{2}[/tex]
