Simplifying Core 3 Compound Angles

[CathyLou]

Hi.

Could someone please tell me the method to use to simplify cosBcosB + sinBsinB?

Any help would be really appreciated.

Thank you.

Cathy

 

[arildno]

Well, isn't that equal to 1??

 

[CathyLou]

Well, isn't that equal to 1??

Yeah, 1 is the answer in the back of the book. I just do not know why. Could you please explain?

Thank you.

Cathy

 

[arildno]

Well, how was cosine and sine to an angle defined to you in the first place?

Perhaps in terms of right-angled triangles?

 

[CathyLou]

Well, how was cosine and sine to an angle defined to you in the first place?

Perhaps in terms of right-angled triangles?

Do you mean by using SOHCAHTOA?

 

[arildno]

Since I'm not English, I don't know what SOHCAHTOA means.

I assume it is related to:
\cos(v)=\frac{adjacentside}{hypotenuse},\sin(v)=\frac{oppositeside}{hypotenuse}

Now, what interpretation of sine and cosine do you get if the hypotenuse equals 1?
(Alternatively, you may have learned about how sine and cosine are defined on the unit circle).


In this case, with the hypotenuse equal to 1, what do we get out of the Pythagorean theorem?