Expert: Sherry Wallin - 11/11/2009

Question
QUESTION: Hi, can you help me in this question please?
It says choosing appropriate values for A and B, verify that
cos(A+B)=cosAcosB - sinAsinB

Thanks

ANSWER: Rabia~
    This is a well known relationship. This is called the sum and difference formula for the cosine function. You go ahead and choose any value for A and B in the range of 0 to 2pi and it will work!

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Thank you...

Also, can you explain how that cofunction identity sin theta = cos (pi/2 - theta) is true?


Answer
Hi Rabia~
   If you look at what happens in the first quadrant with the sine function and the cosine function you will see why this is true. The cos 0 = 1 while the sin 0 = 0. At 90 degrees, the cos 90 = 0 and the sin 90 = 1. So from 0 to 90 degrees the cosine goes from 1 to 0 in increments and the sine goes from 0 to 1 in increments. It just so happens that this occurs in the same ratio and that halfway to 90 degrees which is 45 degrees both the sine function and the cosine function have the same value. When I teach this I tell students that the sine and cosine are related like cousins. It is also true when you take the sine of any angle and square it and take the cosine of that same angle and square it and add those two values that you will always get 1 and that is another relation (relative). I hope this helps.

Math Prof