SOLUTION: Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5 (Both are in Quadrant II.) sin (u + v)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5 (Both are in Quadrant II.) sin (u + v)      Log On


   

Question 1060448: Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5 (Both are in Quadrant II.) sin (u + v)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5 (Both are in Quadrant II.) sin (u + v)
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

I am going to use the formula

sin(u+v) = sin(u)*cos(v) + cos(u)*sin(v).     (*)


For it, in addition to the given values  sin(u) = 5/13 and cos(v) = -3/5  I need to know  cos(u)  and  sin(v).


1.   cos(u) = -sqrt%281-sin%5E2%28u%29%29 = -sqrt%281-%285%2F13%29%5E2%29 = -sqrt%281+-+%2825%2F169%29%29 = -sqrt%28%28169-25%29%2F169%29 = -sqrt%28144%2F169%29 = -12%2F13.

    The sign "-" is at the sqrt since cosine is negative in QII.


2.  sin(v) = sqrt%281-cos%5E2%28v%29%29 = sqrt%281-%28-3%2F5%29%5E2%29%29 = sqrt%281-9%2F25%29%29 = sqrt%2816%2F9%29 = 4%2F5.

    The sign "+" is at the sqrt since sine is positive in QII.


3.  Now you have everything to use the formula (*). Substitute all given and found values into (*). You will get

    sin(u+v) = sin(u)*cos(v) + cos(u)*sin(v) = %285%2F13%29%2A%28-3%2F5%29+%2B+%28-12%2F13%29%2A%284%2F5%29 = -15%2F65+-+48%2F65 = -63%2F65.


Answer.  sin(u+v) = -63%2F65.


Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5 (Both are in Quadrant II.) sin (u + v)
Problem # 1060297 "asked" for sec (v - u). That answer was given to you. Why can't you follow the same steps to obtain sin (u + v)?

Why do you want someone to do everything for you? You have to make an effort, and give someone else a chance to get their problem solved. 

Don't you think you're being UNFAIR?