Trigonometry, different products of sine and cosine

[Trail_Builder]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I don't really know any trigonometric identies and I am guessing that's where the solution lies :S

 

[antonantal]

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

 

[Trail_Builder]

:S

sorry i still don't know how i would use it

 

[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?

 

[HallsofIvy]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I don't really know any trigonometric identies and I am guessing that's where the solution lies :S

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

:S

sorry i still don't know how i would use it

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

 

[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.