SOLUTION: cos a = 4/9, a in Q1, and tan b = -5/4, b in Q2. Find sin (a+b), cos (a+b), tan (a+b)

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Question 927606: cos a = 4/9, a in Q1, and tan b = -5/4, b in Q2.
Find sin (a+b), cos (a+b), tan (a+b)

Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
cos a = 4/9, a in Q1, and tan b = -5/4, b in Q2.
Find sin (a+b), cos (a+b), tan (a+b)
------------
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
---------
cos(a+b) = cos*cos - sin*sin
---------
tan = sin/cos

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
If we need exact values, we need to use the trigonometric identities
and ,
so as a first step, we are going to find exact values for and .

in Q1.
In quadrant 1, sine and cosine are positive , and we know that , so


in Q2 means
From the red right rectangle, we calculate
and .

Now,


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