SOLUTION: please help me solve this problem using exact values {{{sinx=2/5}}} and {{{cosx<0}}} I must use identities to find cosx,tanx,cotx,secx, and cscx.

Algebra ->  Trigonometry-basics -> SOLUTION: please help me solve this problem using exact values {{{sinx=2/5}}} and {{{cosx<0}}} I must use identities to find cosx,tanx,cotx,secx, and cscx.      Log On


   

Question 674086: please help me solve this problem using exact values sinx=2%2F5 and cosx%3C0 I must use identities to find cosx,tanx,cotx,secx, and cscx.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
using exact values sinx=2%2F5 and cosx%3C0 I must use identities to find cosx,tanx,cotx,secx, and cscx.
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Since sin is positive and cos is negative the angle is in QII.
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Since sin(x) = 2/5, y = 2 and r = 5
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Solve for "x":
x = sqrt(r^2-y^2) = sqrt(25-4) = sqrt(21)
But x is in QII so x = -sqt(21)
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sin = y/r = 2/5
cos = x/r = -sqrt(21)/5
tan = y/x = -2/sqrt(21)
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csc = r/y = 5/2
sec = r/x = -5/sqrt(21)
cot = x/y = -sqrt(21)/2
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Cheers,
Stan H.