Find the exact value of sin(x+y) if cos x = 8/17 and sin y= 12/37

621 /629

Step-by-step explanation:

The formula for sin (x+y) is sin x cosy + cos x sin y.

                                                      opposite side

If sin y  12/37 (which is equal to )  we can find the length

                                                        hypotenuse

of the adjacent side as follows.  Representing the adjacent side by x, we get

37^2 = x^2 + 12^2 (following the Pythagorean Theorem).

Then 1369 = x^2 + 144, or x^2 = 1225, so that x must be +√1225, or +35.

Thus, the cosine of y is (adj side) / (hypo) = 35/37.

                                                    √(17^2 - 8^2)       √225

Similarly, the sine of angle x is =   = 15/17

                                                             17                     17

In summary, sin x = 15/17; cos x = 8/17; sin y = 12/37 and cos y =35/37.

We now substitute these values into the formula

sin (x+y) is sin x cosy + cos x sin y:

sin (x+y) = (15/17)(35/37) + (8/17)(12/37)

                      525               96               621

              = + = = 621 /629

                      629              629              629