anonymous
  • anonymous
Find cos θ if csc θ = 2 and θ is in quadrant II.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
OK so... Sin θ = 1/Csc θ so it would be 1/2 which is O/H? So the mesurements can be calculated using x^2 + y^2 = r^2?
anonymous
  • anonymous
θ=60
anonymous
  • anonymous
as......... if ....secθ=2 hence ...1/cosθ=2 cosθ=1/2 sin(90+θ)=1/2

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anonymous
  • anonymous
hence .......θ=60
dumbcow
  • dumbcow
csc = 1/sin --> 1/sin = 2 --> sin = 1/2 cos^2 = 1-sin^2 cos^2 = 1-(1/2)^2 cos^2 = 3/4 cos = sqrt3/2
anonymous
  • anonymous
thought since sin would = 1/2 and csc = 2 then wouldn't it be 30?
dumbcow
  • dumbcow
no theta = 150 since in quad 2
anonymous
  • anonymous
of it's cosec θ then dumbcow is right
anonymous
  • anonymous
yea sqrt(3)/2
anonymous
  • anonymous
would it be negative since it's in the II quadrant? and only thing positive in II quadrant is Sin and CSC?
anonymous
  • anonymous
sry fakshon ...i consideed it as sec θ
dumbcow
  • dumbcow
correct, cos would be negative :)
dumbcow
  • dumbcow
@shivamsinha it happens :)
anonymous
  • anonymous
yep yep it's all good.
anonymous
  • anonymous
thanks for the help.

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