SOLUTION: Given sin(a) = 5/8 and a is in quadrant 2 and sin (b) = -7/9 and b is in quadrant 3. Use sum and difference formulas to find the following: Note: You are not allowed to use decim

Algebra ->  Trigonometry-basics -> SOLUTION: Given sin(a) = 5/8 and a is in quadrant 2 and sin (b) = -7/9 and b is in quadrant 3. Use sum and difference formulas to find the following: Note: You are not allowed to use decim      Log On


   

Question 1183305: Given sin(a) = 5/8 and a is in quadrant 2 and sin (b) = -7/9 and b is in quadrant 3. Use sum and difference formulas to find the following:
Note: You are not allowed to use decimals in your answer.
tan(a+b) =
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given:
sin%28a%29+=+5%2F8 and a is in quadrant 2
sin%28a%29++=opp%2Fhyp=5%2F8 =>opp=5 and+hyp=8
adj=sqrt%288%5E2-5%5E2%29
adj=sqrt%2864-25%29
adj=sqrt%2839%29
cosine in quadrant 2 is negative
cos%28a%29+=-adj%2Fhyp+=-sqrt%2839%29%2F8

and sin+%28b%29+=+-7%2F9 and b is in quadrant 3.
sin+%28b%29+=+-7%2F9 =>opp=7, hyp=9
adj=sqrt%289%5E2-7%5E2%29=sqrt%2832%29=4sqrt%282%29
cos in quadrant 3 is negative
cos%28b%29=-adj%2Fhyp
cos%28b%29=-4sqrt%282%29%2F9

so, we have:
sin%28a%29+=+5%2F8+ and cos%28a%29=-sqrt%2839%29%2F8
sin+%28b%29+=+-7%2F9 and cos%28b%29=-4sqrt%282%29%2F9

then
tan%28a%2Bb%29+=sin%28a+%2B+b%29%2Fcos%28a+%2B+b%29







tan%28a%2Bb%29+=%287sqrt%2878%29+-+40%29%2F%28sqrt%282%29+%2835+%2B+4sqrt%2878%29%29%29

tan%28a%2Bb%29+=%281%2F23%29+%281792sqrt%282%29+-+405sqrt%2839%29%29