Question

If `sin theta = 21/29`, what is `cos theta` and `tan theta`?

Answer 1

`costheta= 20/29`

and `tantheta=20/21`

details follow...

Explanation:

It is common to express the three trig functions as ratios involving the sides of a right-angle triangle, whose sides are called the adjacent side, the opposite side and the hypotenuse.

In the diagram below, these are a, b, and c respectively.

![

As the diagram shows, each trig function can be expressed as a ratio:

`sintheta=b/c`, so in your problem, we can assign the value 21 to `a`, and 29 to `c`.

By the Pythagorean theorem,

`b=sqrt(c^2-a^2) = sqrt(29^2-21^2) = sqrt400 = 20`

So, `costheta= a/c = 20/29`

and `tantheta=b/a = 20/21`