[MOVED] evaluate tan(cos^-1(x))

[dagr8est]

Hi, I am told to evaluate tan(cos^-1x). So:

tan(cos^-1x)
=sin(cos^-1x)/cos(cos^-1x)
=sin(cos^-1x)/x

Can I simplify this further? The only other thing I can think of doing is:

=sin(pi/2-sin^-1x)/x

but that doesn't seem to help.

 

[stapel]

By definition, "cos^-1(x) = y" means that, for some angle measure y, cos(y) = x.

Draw a right triangle. (Scale is not particularly important.) Label the base angle opposite the right angle as "y". Then note that x = x/1, and label the "adjacent" and "hypotenuse" sides from the given cosine ratio.

Use the Pythagorean Theorem to find the expression for the length of the "opposite" side.

Since cos^-1(x) = y, then tan(cos^-1(x)) = tan(y).

Read the tangent value from the triangle.

Eliz.