# Trigonometry, different products of sine and cosine

1. Sep 22, 2007

### Trail_Builder

1. The problem statement, all variables and given/known data

There is a right angled triangle, with the following angles, a, b, and 90deg.

If a < b, how many different values are there among the following expressions?

sin a sin b, sin a cos b, cos a sin b, cos a cos b

2. Relevant equations

3. The attempt at a solution

I dont really know any trigonometric identies and im guessing thats where the solution lies :S

Last edited: Sep 23, 2007
2. Sep 22, 2007

### antonantal

Here is a trigonometric identity: sin(x) = cos(90 - x)
Try to use it.

3. Sep 23, 2007

### Trail_Builder

:S

sorry i still dont know how i would use it

4. Sep 23, 2007

### antonantal

What is the sum of the 3 angles in a triangle?
And if you know that one of them is a right angle, then what is the sum of the other 2?

5. Sep 23, 2007

### HallsofIvy

Staff Emeritus
The point is that sin(a)= cos(b) and sin(b)= cos(a).

6. Oct 9, 2007

### dasher

there are 3 different values there. the oiint in telling you that b>a is to make sure you know that b does not equal to a. because, is b=a, the values for all the expressions will be the same. but in this case, since the 2 angles are different, sina=cosb. also, sinb=cosa. if you don't get this, try drawing out a right-angled triangle and label it's angles. use 3,4,5 as the length of its sides. 5 is the hypothenus. then sub the values into the expressions. you will find that sina sinb=cosa cosb.