SOLUTION: Using a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. The problem I ha

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Question 687593: Using a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. The problem I have to solve is sin[tan-1x] *Not negative one, the inverse of tan.
Answer by stanbon(75887) About Me  (Show Source):
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Using a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. The problem I have to solve is sin[tan-1x] *Not negative one, the inverse of tan.
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Let theta be tan^-1(x)
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Since tan(theta) = x/1, x = opp and 1 = base
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Find hypotenuse: h = sqrt[x^2 + 1^2]
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Therefore sin(theta) = opp/hypot = x/sqrt(x^2+1)
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Cheers,
Stan H.