all you need is the sum formula for cosines.
in other words,
cos(A+B) = .957269
A+B = 16.81°
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.
So I'm pretty lost on how to even begin this problem. I do know the product-to-sum identities such as cos(a)cos(b)=1/2(cos(a+b)+cos(a-b))
Any help is greatly appreciated!
in other words,
cos(A+B) = .957269
A+B = 16.81°
Sum and difference identities is what I meant to say:
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
cos(A)cos(B) - sin(A)sin(B) = 0.957269
Using the product-to-sum identity for cosine, we can rewrite the left-hand side of the equation:
[(1/2)(cos(A + B) + cos(A - B))] - sin(A)sin(B) = 0.957269
Next, let's substitute the product-to-sum identity for sine:
[(1/2)(cos(A + B) + cos(A - B))] - [(1/2)(cos(A - B) - cos(A + B))] = 0.957269
Now, simplify the equation:
(1/2)(cos(A + B) + cos(A - B) - cos(A - B) + cos(A + B)) = 0.957269
The cos(A - B) and -cos(A - B) terms cancel out, leaving:
(1/2)(2cos(A + B)) = 0.957269
Simplifying further:
cos(A + B) = 1.914538
Now, to express A in terms of B, we need to use the inverse cosine function (arccos or cos^(-1)). Taking the inverse cosine of both sides:
A + B = arccos(1.914538)
Since we want to express A in terms of B, we need to isolate A:
A = arccos(1.914538) - B
Now we can plug in the value of B to find the specific value for angle A. Remember to work in degrees and round the final answer to two decimal places.
Note: It's important to mention that the equation provided (cos(A)cos(B)-sin(A)sin(B)=0.957269) does not have unique solutions. The angle values depend on the chosen value for B.