double angle formulas

[young fiber]

I just need help figuring out how to solve the circled three problems step by step

[wise flame]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
   +close

[tawny delta]

3. x=2, y=-5
   hyp = sqrt(2²+(-5)²) = ...
   then use the double angle formulas
4. x is in the 3rd quadrant, so
   only tan and cot is positive
   then use the double angle formulas
5. cot(x) = adj/opp = cos(x)/sin(x) = 2/1
   hyp = sqrt(2²+1²) = sqrt(5)
   since cos(x) < 0 and 2 > 0,
   therefore sin(x) < 0, cuz
   negative/negative = positive
   sin(x) = opp/hyp = 1/sqrt(5)
   but sin(x) < 0, hence:
   sin(x) = -1/sqrt(5)

notes:
sin(2x) = 2 sin(x) cos(x)
cos(2x) = cos²(x)-sin²(x) = 2 cos²(x)-1 = 1-2 sin²(x)
tan(2x) = 2 tan(x)/(1-tan²(x))