SOLUTION: If cos(theta) = sqrt(2)/-3 and theta has its terminal side in Quadrant 2, find the exact value of tan(2theta)

Question 1033301: If cos(theta) = sqrt(2)/-3 and theta has its terminal side in Quadrant 2, find the exact value of tan(2theta)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If cos(theta) = sqrt(2)/-3 and theta has its terminal side in Quadrant 2, find the exact value of tan(2theta)
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Since cos = x/r and since x is negative in QII, x = -sqrt(2) and r = 3
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Then y = sqrt[3^2-(sqrt(2))^2] = sqrt(7)
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tan = y/x = -sqrt(7)/sqrt(2) = -sqrt(7/2)
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Ans: Formula:: tan(2t) = 2tan(x)/(1-tan^2(x))
Your Problem:
tan(2t) = 2[-sqrt(7/2)]/[1-(7/2)] -2sqrt(7/2)/(-5/2) = (4/5)sqrt(7/2)
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Cheers,
Stan H.
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