Compute or solve the following in radians without a calculator

Question

a. csc x=2, pi/2 ≤ x ≤ pi

b. cot x= -1 , 3pi/2 ≤ x ≤ 2pi

Thanks!

Answer 1

At this point of your study of trig, you should be familiar with the ratio of sides of the 30-60-90 degree triangle which would be 1 : √3 : 2 respectively, as well as the
45-45-90 triangle with sides in the ratio of 1 : 1 : √2

with csc x=2, pi/2 ≤ x ≤ pi , you know
sinx = 1/2 and x is in quadrant II, where the sine is positive
from you triangle you know sin π/6 = 1/2 , (sin 30° = 1/2)
so x = π - π/6 = 5π/6

do the other question in the same way, by using the other triangle