SOLUTION: Find the exact value of tan (a + b) if cos a = -3/5, sin b = 5/13, 90° < a < 180°, and 90° < b < 180°. Do not round.

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Question 1014959: Find the exact value of tan (a + b) if cos a = -3/5, sin b = 5/13, 90° < a < 180°, and 90° < b < 180°. Do not round.

Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
sec a = -5/3 ==> 1 + tan^2 a = 25/9 ==> tan^2 a = 16/9 ==>tan a = -4/3 (Angle a is in the 2nd quadrant because 90° < a < 180°.)
sin b = 5/13 ==> 1+ cot^2 b = 169/25 ==> cot^2 b = 144/25 ==> cot b = -12/5 (Angle b also in the 2nd quadrant because 90° < b < 180°.)
==> tan b = -5/12.
==>
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
Find the exact value of tan (a + b) if cos a = -3/5, sin b = 5/13, 90° < a < 180°, and 90° < b < 180°. Do not round.
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1.  Use the addition formula for tangent:  tan(a + b) = 

    (see the lesson Addition and subtraction formulas in this site).


2.  sin(a) =  =  = . . . = .

     Notice that the sign of the square root is chosen accordingly with the location of the angle "a" in the Quadrant 2.


3.  cos(b) = - = - = . . .  = .

     Notice that the sign of the square root is chosen accordingly with the location of the angle "b" in the Quadrant 2.


4.  Now,  tan(a) =  =  :  =    and

          tan(b) =  =  :  = .


5.  Finally,  tan(a+b) =  =  =  =  = .


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