Sum and difference identities

[icelated]

I have a question that i cannot possibly solve. Its in the suppliment package that dont have a solution.

Suppose that cos(A) = 0.22, sin(A) = -0.98, cos(B)= 0.60 and sin(B)= 0.85. Use the formulas for sin(A +-B) and cos(A+-B) to find exact values

a) sin(A-B)

b) cos(A+B)


This is what i think i need to do for a

Sin(-.98-.85)

sin(-.098)cos(0.85) - sin(0.85)cos(-0.98)
thats all i can do since they are not angles.

i need some serious help with this. thank you

 

[nikkor180]

You are given the sine and cosine of both A and B, and asked, in #1, to find the sin(A-B). The provided identity gives sin(A-B) = sin(A)cos(B) - sin(B)cos(A). Making the appropriate substitutions gives sin(A-B) = -0.98(0.6) - 0.85(0.22) approx -0.775. Note that your calculations will provide approximations only, as the given values are approximated. To see this, note that said values do not satisfy cos^2(x) + sin^2(x) = 1. That said, I believe the final calculations should be rounded to one significant figure.

Regards,

Rich B.