SOLUTION: Find tan(s+t) if cos s = (-1/5), sin t = 3/5, and s and t are in quadrant 2. I have ready substituted values into the tan sum identity, but I'm having trouble with the arithmetic.

Algebra ->  Trigonometry-basics -> SOLUTION: Find tan(s+t) if cos s = (-1/5), sin t = 3/5, and s and t are in quadrant 2. I have ready substituted values into the tan sum identity, but I'm having trouble with the arithmetic.      Log On


   

Question 861248: Find tan(s+t) if cos s = (-1/5), sin t = 3/5, and s and t are in quadrant 2.
I have ready substituted values into the tan sum identity, but I'm having trouble with the arithmetic.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find tan(s+t) if cos s = (-1/5), sin t = 3/5, and s and t are in quadrant 2.
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tan%28s%2Bt%29=%28tan%28s%29%2Btan%28t%29%29%2F%281-tan%28s%29tan%28t%29%29
...
cos(s)=-1/5

tan(s)=sin/cos=-√24/1=-√24
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sin(t)=3/5 (working with a (3-4-5) reference right triangle in quadrant 2)
cos(t)=-4/5
tan(t)=sin/cos=-3/4
...
tan%28s%2Bt%29=%28tan%28s%29%2Btan%28t%29%29%2F%281-tan%28s%29tan%28t%29%29
tan(s+t)=(-√24-3/4)/(1-√24*(3/4)
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calculator check:
cos(s)=-1/5
s≈101.54 deg
sin(t)=3/5
t≈143.13
s+t≈244.67
tan(s+t)=tan(244.67)≈2.112…
exact value as calculated=(-√24-3/4)/(1-√24*(3/4)≈2.112...
note: let me know if my solution is correct, helpful and understandable