find sin(x+y) & cos(x-y), given sinx=(-3/5) & cosy=(-7/25)

Question

fibonaccichick666 · Answer

So, what is the definition of sine?

anonymous · Answer

In what terms? Like its actual definition, its identities, etc.

fibonaccichick666 · Answer

actual definition please :)

anonymous · Answer

The sine is the ratio of the length of the side that is opposite an angle divided by the length of the hypotenuse.

fibonaccichick666 · Answer

very good, we can shorten that to sine theta= opp over hyp right?

anonymous · Answer

Yeah.

fibonaccichick666 · Answer

alright so if $sin x=\frac {-3}{5}$ what is the -3 and what is the 5?  Could you draw a picture to illustrate what they are?

anonymous · Answer

|dw:1398310204447:dw|

fibonaccichick666 · Answer

label the angle too please

anonymous · Answer

|dw:1398310320236:dw|

fibonaccichick666 · Answer

alright, so now ignore the minus for a moment.  What is the measure of the 3rd side?

anonymous · Answer

It'd be 4.

fibonaccichick666 · Answer

good, so now, you could find the angle and do the same idea for the other and then just physically add the angles then compute the sin(x+y) and cosine that way, but that is just too much work, so let's take the easy way out.  Do you know the summation identities for sine and cosine?