Question

solve each equation for è, giving a general formula for all of the solutions:

6. tanè=-1
7. sin(è/2)=1/2

Please show step by step on how to solve these. Im not sure on how to do them. Thank you for your help!

Answer 1

tanx = -1

you need to know that:
tan pi/4 = 1
tan x is negative in QII and QIV

so, tanx = -1 if x = pi-pi/4 = 3pi/4 or 2pi-pi/4 = 7pi/4

sin(x/2) = 1/2
sin pi/6 = 1/2
sin x is positive in QI and QII

so, sinx = 1/2 if x = pi/6 or pi-pi/6 = 5pi/6

Answer 2

Oops, that would be x/2 = pi/6 or 5pi/6

so, x = pi/3 or 5pi/3