Question

If sinA=0.25, cosA=0.97, sinB=0.45, and cosB=0.89, what is sin(A+B)?

Answer 1

Using the sine addition formula, sin(A+B) = sinA cosB + cosA sinB, and substituting the given values, we find that sin(A+B) is approximately 0.659.

Step-by-step explanation:

To find sin(A+B), we use the sine addition formula, which states that sin(A+B) = sinA cosB + cosA sinB. Given that sinA=0.25, cosA=0.97, sinB=0.45, and cosB=0.89, we can substitute these values into the formula:

sin(A+B) = (0.25)(0.89) + (0.97)(0.45)

sin(A+B) = 0.2225 + 0.4365

sin(A+B) = 0.659

This calculation shows that sin(A+B) is approximately 0.659.