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Trigonometric function help please?

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Assume that 0 < thea< pi/2. Find an expression for the indicated trigonometric function.

Let x = 3 tanthea . Find sec thea.

Help please??
asked Apr 12, 2013 in TRIGONOMETRY by homeworkhelp Mentor

1 Answer

0 votes

0 < θ < π/2

x = 3tanθ

Divide each side by 3

x / 3 = tanθ

Take square to each side

x2 / 32 = tan2θ

But sec2θ = 1 + tan2θ

sec2θ = 1 + x2 / 9

sec2θ = (9 + x2 ) / 9

Take square root to each side

secθ = √(9 + x2) / √9

secθ = √(9 + x2) / 3.

answered Apr 12, 2013 by diane Scholar

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