pi<theta<2pi and tan theta = (sqrt 5)/2 find the values of the other 4 trig functions

Question

Cant find a similar type of problem on google. Textbook didn't help.

Answer 1

tangent=opposite/adjacent

tanθ=√5/2

draw a right triangle in the third quadrant with one leg being part of the negative x-axis and the other leg is a vertical line perpendicular to the x-axis

the hypotenuse is a line drawn from the origin down and to the left (southwest direction)

the angle θ is formed by the hypotenuse and the x-axis

use the Pythagorean Theorem

h^2=2^2+(√5)^2

h^2=4+5

h^2=9

h=√9

h=3

the hypotenuse is 3, the opposite leg is √5 and the adjacent leg is 2

sin=opp/hyp

cos=adj/opp

csc=1/sin

sec=1/cos

cot=1/tan

now you can get the rest of the answers