# Sum and diggerence identities

• February 9th 2009, 07:01 AM
mj.alawami
Sum and diggerence identities
Angles for sum and difference identities?

how to find the angle of the sum and difference identities
for example sin 15 =(60-45) form where did the 60 and 45 come from and how did you get them in order to solve the problem
Why can't we use instead of 60 -45 >>>>>>10 +5?
• February 9th 2009, 08:52 AM
ixo
This should be the identity that will solve it..
$\sin(u\pm m) = \sin(u)\cos(m)\pm \cos(u)\sin(m)$
• February 9th 2009, 08:58 AM
masters
Quote:

Originally Posted by mj.alawami
Angles for sum and difference identities?

how to find the angle of the sum and difference identities
for example sin 15 =(60-45) form where did the 60 and 45 come from and how did you get them in order to solve the problem
Why can't we use instead of 60 -45 >>>>>>10 +5?

Hi mj,

The reason we want to use 60 and 45 is because they are special angles which we can easily find the trig functions for without using a calculator.

From the unit circle, you should know that:

$\sin 60=\frac{\sqrt{3}}{2}$

$\cos 60=\frac{1}{2}$

$\sin 45=\cos 45=\frac{\sqrt{2}}{2}$

Now just substitute these values into your angle difference identity:

$\sin(60-15)=\sin 60 \cos 45 - \cos 60 \sin 45$

And simplify.