Suppose cos(x) = u, how do you write tan(x) in terms of x?

Question

6592 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-16T09:27:37

$tan(x) = (sin(x))/(cos(x))$

Remember from SOH CAH TOA that

$costheta = ("Adjacent")/("Hypotenuse")$

We can use this to construct a triangle.

enter image source here

From the triangle, we see that

$tan(x) = (sqrt(1-u^2))/u$

$tan(x) = (sqrt(1-cos^2(x)))/(cos(x)) = (sqrt(sin^2(x)))/cos(x)$

$therefore tan(x) = (sin(x))/(cos(x))$