SOLUTION: Thank you!! Struggling with this. Given sinx=-(2)/(3), 180 degrees less than or equal to, x, less than or equal to 270 degrees and cosy=(4)/(7), 270 degrees less than or equal

Question 1154938: Thank you!! Struggling with this.
Given sinx=-(2)/(3), 180 degrees less than or equal to, x, less than or equal to 270 degrees and cosy=(4)/(7), 270 degrees less than or equal to, y, less than or equal to 360 degrees, find the exact value of tan(x+y).
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

(1a) Given sinx = -2/3 in quadrant III, use sin^2 + cos^2 = 1 to find cosx, and give it the negative value since cosine is negative in quadrant III.

(1b) Given cosy 4/7 in quadrant IV, use sin^2 + cos^2 = 1 to find sinx, and give it the negative value since sine is negative in quadrant IV.

(2a) Find sin(x+y), using sin(x+y) = sinx*cosy+cosx*siny

(2b) Find cos(x+y), using cos(x+y) = cosx*cosy-sinx*siny

(3) Find tan (x+y), using tan(x+y) = sin(x+y)/cos(x+y)

If you find you are still struggling with this, re-post showing the work you have done.

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