Sum and difference identities help?

May 2016
3
0
USA
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The following relationship is known to be true for two angles A and B:

cos(A)cos(B)-sin(A)sin(B)=0.957269

Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places.
Enter your answer as an expression. Be sure your variables match those in the question.

So I'm pretty lost on how to even begin this problem. I do know the sum and difference identities such as cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

Any help is greatly appreciated!
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
So from that identity you know that \(\displaystyle cos(A+ B)= 0.957269\). The rest is easy- what is A+ B equal to? (The problem says "express A in terms of angle B". You are not asked to find numerical values for A and B separately- and you can't.)
 
May 2016
3
0
USA
I tried taking inverse cosine of 0.957269 and got about 16.81 degrees since we're asked to work in degrees. I typed that into the math site and it doesn't like my answer?
 
May 2016
3
0
USA
I'm sorry I'm still confused with what you're tying to say,
I tried taking inverse cosine of 0.957269 and got about 16.81 degrees since we're asked to work in degrees. I typed that into the math site and it doesn't like my answer
 

romsek

MHF Helper
Nov 2013
6,725
3,030
California
I'm sorry I'm still confused with what you're tying to say,
I tried taking inverse cosine of 0.957269 and got about 16.81 degrees since we're asked to work in degrees. I typed that into the math site and it doesn't like my answer
so $A+B=16.81^\circ$

$A=16.81^\circ - B$

did you type the last bit in or just the $16.81^\circ$ ?