Question

PLZ ANSWER AND SHOW WORK TY :D

Answer 1

`-(√(21))/(2)`

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)

`(-2)^2+o^2=5^2;4+o^2=25;o^2=21;o=√(21)`

tanx =
`(√(21))/(-2)=-(√(21))/(2)`