SOLUTION: Given cos(a) = 1/2, tan(b) = -3/2, 0 < a < ((pi)/2), and ((pi)/2) < b < pi, find sin(a+b), cos(a-b), and tan(a+b)

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Question 1188397: Given cos(a) = 1/2, tan(b) = -3/2, 0 < a < ((pi)/2), and ((pi)/2) < b < pi, find sin(a+b), cos(a-b), and tan(a+b)
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!
Sunday, April 2, 2017
7:06 PM


If you know the cosine of an angle and the quadrant where the terminal ray lies, then you can calculate the sine of the angle by:



and then choose the sign using the fact that the sine is positive in QI and QII, and negative in QIII and QIV.

Once you know the sine and cosine, you can calculate the tangent by using:



If you know the tangent of an angle to be and the Quadrant, then you can find both the sine and cosine by:










And then solve for the sine selecting the sign based on the quadrant.

Similarly, the cosine can be determined by solving:



and noting that cosine is positive in QI and QIV, negative in QII and QIII.

The sine, cosine, and tangent of the sum and difference of two angles:







John

My calculator said it, I believe it, that settles it

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