SOLUTION: How do I find tan(sin^-1 1/3) by using the unit circle? I know you have to find the sin of 1/3 by looking in quadrant 1 or 4. and X is the cos and Y is the sin but I can't find 1/3

Question 736047: How do I find tan(sin^-1 1/3) by using the unit circle? I know you have to find the sin of 1/3 by looking in quadrant 1 or 4. and X is the cos and Y is the sin but I can't find 1/3 on my unit circle... I also know that Tan is sin over cos but do you divide the sin and the cos to get tan? I have no idea what I'm doing. Please explain it to me? Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do I find tan(sin^-1 1/3) by using the unit circle?
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You have a certain angle.
Its sin = y/r = 1/3.
So y = 1 and r = 3
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The tan is y/x so you have to find "x":
x = sqrt[r^2-y^2] = sqrt[9-1] = 2sqrt(2)
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Therefore tan(your angle) = y/x = 1/sqrt(8) = (1/8)sqrt(8)
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Note: You don't have to know the angle.
Cheers,
Stan H.
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