SOLUTION: What is sin if is in standard position, its terminal side lies in quadrant IV, and sec=√3? a.√2/2 b.-√6/3 c.√3/3 d.-√3/3

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Question 810122: What is sin if is in standard position, its terminal side lies in quadrant IV, and sec=√3?
a.√2/2
b.-√6/3
c.√3/3
d.-√3/3


Found 2 solutions by lwsshak3, MathTherapy:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
What is sin if is in standard position, its terminal side lies in quadrant IV, and sec=√3
***
sec=√3=1/cos
cos=1/√3
sin=-√(1-cos^2)=-√(1-1/3)=-√(2/3)
none of given ans. match this solution

Answer by MathTherapy(10810) About Me  (Show Source):
You can put this solution on YOUR website!
What is sin if is in standard position, its terminal side lies in quadrant IV, and sec=√3?
a.√2/2
b.-√6/3
c.√3/3
d.-√3/3

sec=√3_____cos θ = 1%2Fsqrt%283%29____cos θ = sqrt%283%29%2F3 = A%2FH = x%2Fr

Therefore, x+=+sqrt%283%29, and r+=+3

y+=+sqrt%28r%5E2+-+x%5E2%29

y+=+sqrt%283%5E2+-+%28sqrt%283%29%29%5E2%29

y+=+sqrt%289+-+3%29

y+=+sqrt%286%29

sin θ = O%2FH = y%2Fr = sqrt%286%29%2F3, but since sin is < 0 in the 4th quadrant, we get: - sin θ = highlight_green%28-+sqrt%286%29%2F3%29 (CHOICE b.)

You can do the check!!

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