SOLUTION: Use the properties of inverse functions to evaluate the expression cos [arcsin (5sqrt29/29)] I was told the answer is 2sqrt29/29 but I can't figure out how. Thanks!

Algebra ->  Test -> SOLUTION: Use the properties of inverse functions to evaluate the expression cos [arcsin (5sqrt29/29)] I was told the answer is 2sqrt29/29 but I can't figure out how. Thanks!      Log On


   

Question 131335: Use the properties of inverse functions to evaluate the expression
cos [arcsin (5sqrt29/29)]
I was told the answer is 2sqrt29/29 but I can't figure out how. Thanks!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
evaluate the expression
cos [arcsin (5sqrt29/29)]
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Sketch a rt. triangle in standard position in the 1st Quadrant.
You have an angle whose sine is (5sqrt(29))/29
So the hypotenuse is 29 and the vertical side is 5sqrt(29)
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Use Pythagoras to solve for the horizontal side (hs)
(hs)^2 = 29^2 -(5sqrt(29))^2
(hs)^2 = 841 - 725
(hs) = 10.77...
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Therefore cos[angle] = 10.77/29
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Cheers,
Stan H.