Question

Suppose sin (t) = (x/5) and the angle t is in the first quadrant. Write algebraic expression for cos (t) and tan (t) in terms of x.

Answer 1

Draw a triangle with a side x and a hypotenuse 5.
Then let the angle opposite of side x be angle t.
We imagine the angle t growing from 0 to pi/2 while keeping the hypotenuse at 5 units.
As we do this, that the side of length x grows too. So the ratio x/5 changes.

Anyways, in this triangle, the remaining side is found using the Pythagorean theorem.
It is sqrt(25 - x^2).

So then we see that for any t between 0 and pi/2, cos t = sqrt(25 - x^2)/5.
And also tan t = x/sqrt(25 - x^2)..

These are the expressions in terms of x you're looking for.

Answer 2

Thank you.