# Trigonometric Equation problem

## Homework Statement

If cos x = a/b and tan x = c/d; where a, b, c do not equal 0, then sin x is.....

(a) bd/ac
(b) bc/ad
(c) ad/bc
(d) ad/bc

## The Attempt at a Solution

The way I see it, if cos x = a/b, then b=hypotenuse.
if tan x = c/d, then d= hypotenuse (two hypotenuse values?) and c = opposite.

Therefore sin x = c/d. I don't know why the answers in the book use products of the vairables in their numerators and denominators.

Please help.

Much thanks in advance.

## Answers and Replies

Related Precalculus Mathematics Homework Help News on Phys.org
Hmmm... Your c) and d) choices are the same..and the tan doesn't involve the hypotenuse.
Are you sure you copied the whole thing right?

Last edited:
HallsofIvy
Science Advisor
Homework Helper
Since
$$tan \alpha= \frac{sin \alpha}{cos \alpha}$$
multiplying on both sides by $cos(\alpha)$ gives

$$sin(\alpha)= cos(\alpha)tan(\alpha)$$
That's all you need.