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5.5.3
Hello, I am hoping you can help me with this problem. I got it wrong on my homework last week and I would like to go back and see what is the proper solution. I tried asking the teacher, but my standard teacher is on maternity leave and the substitute couldn't explain it very well. I was hoping you could show me the answer, as well as how you got that answer. Thank you for your time and assistance! -John

The question is:
Find the EXACT value (in fractional form) of sin(u + v), given that sin u = 11/61 and cos v = -40/41 and both u and v are in Quadrant 2

sin(u+v)=sin u cos v + cos u sin v
11/61*-40/41 + -60/61*9/41
Draw a right triangle in the 2nd quadrant and label the vertical leg 11 and the hypotenuse 61. Use Pythaorus' Theorem to get the other leg measure which is 60. Since the cos(angle) is adjacent over the hypotenuse we have the
cos u = 60/61 but it is negative (-60/61) because the cos(angle) is negative in quadrant 2. Again draw a right triangle in quadrant 2 but label the adjacent side (horizontal) 40 and hypotenuse 41. Again use Pythagorus' Theorem to get the vertical side measure of 9, thus sin v = 11/61

Now substitute all values into the formula for sin(u+v) getting an exact value of -980/2501
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