SOLUTION: given that A is obtuse and that tan A= -1/2, find the value of cos A and of sin A

Question 847482: given that A is obtuse and that tan A= -1/2, find the value of cos A and of sin A

Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
tan A = - 1/2
tan^-1 A = tan^-1(-1/2) = -26.56 degrees
We know that A is between 0 and 180 degrees, so the angle formed with 180 is 180 - 26.56 = 153.48 degrees.
From there we can find sin(153.48 degrees ) = 0.45 and cos(153.48 degrees) = -0.89.
Let's check and make sure this works.
We know tan(A) can only be negative in the 2nd and 4th quadrants. Since we're only concerned with the 1st and 2nd quadrants, we know that A must be in the 2nd quadrant. In the 2nd quadrant we expect that cos(A) is negative while sin(A) is positive since cosine refers to our x position while sine refers to our y position. The signs of our answers are in line with this. We also know tan(A) = sin(A)/cos(A). So 0.45/-0.89 = -.5056 which is close enough to -1/2. I'm okay with this because this was a result of rounding.
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