Question

Given sinx=-3/5 and x is in quadrant 3, what is the value of tan(x/2)?

Answer 1

sin^2 + cos^2 = 1
(-3/5)^2 + cos^2 = 1
cos^2 = 1-9/25 = 16/25
cosx = -4/5 (neg because in quad 3)

Use Half angle identity for tangent
tan(x/2) = sqrt((1-cos)/(1+cos))
= sqrt((1+4/5)/(1-4/5))
=sqrt(9/5)/(1/5))
= sqrt(9)
= 3

Answer 2

thank you!

Answer 3

no problem,
it might be -3 though since x/2 would be in quadrant 2

Answer 4

for these problems i suggest making a trig reference sheet, thats what i do, no way i can memorize all these formulas