SOLUTION: Could you please help me with the following problem, Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the given

Algebra ->  Trigonometry-basics -> SOLUTION: Could you please help me with the following problem, Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the given       Log On


   

Question 1012334: Could you please help me with the following problem,
Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the given inverse trigonometric function
tan(arccos 2x)
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use a right triangle to write the following expression as an algebraic expression.
Assume that x is positive and in the given inverse trigonometric function tan(arccos 2x)
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Let alpha = arccos(2x).

It means that cos%28alpha%29 = 2x and alpha lies in the 1st or in the 2nd quadrant.

We need to express tan%28alpha%29 via x.


Since cos%28alpha%29 = 2x, sin%28alpha%29 = sqrt%281+-%282x%29%5E2%29 = sqrt%281-4x%5E2%29.

Therefore, tan%28alpha%29 = %28sin%28alpha%29%29%2F%28cos%28alpha%29%29 = %28sqrt%281-4x%5E2%29%29%2F%282x%29.

Answer. tan%28alpha%29 = %28sqrt%281-4x%5E2%29%29%2F%282x%29.

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Your formulation is not perfect.
The right formulation is

"Find tan%28alpha%29 if arccos%28alpha%29 = 2x."