SOLUTION: The question said find the exact value of each of the following under the given conditions Sin a = 3/5,0 < a < pi/2; cos b= 4 radical97/97,-pi/2<b<0 1.sin (a+b) 2 cos(a+b

Algebra ->  Trigonometry-basics -> SOLUTION: The question said find the exact value of each of the following under the given conditions Sin a = 3/5,0 < a < pi/2; cos b= 4 radical97/97,-pi/2<b<0 1.sin (a+b) 2 cos(a+b      Log On


   

Question 929156: The question said find the exact value of each of the following under the given conditions
Sin a = 3/5,0 < a < pi/2; cos b= 4 radical97/97,-pi/2
1.sin (a+b)
2 cos(a+b)
3 sin (a-b)
4 cos(a-b)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the exact value of each of the following under the given conditions
Sin a = 3/5,0 < a < pi/2;
cos b= 4 radical97/97,-pi/2 < b < 0

1.sin (a+b)
sin(A+B) = sin(A)cos(B) + sin(B)cos(A)
sin(A) = 3/5
cos%28A%29+=+sqrt%281+-+sin%5E2%28A%29%29+=+sqrt%281+-+9%2F25%29+=+4%2F5
cos(A) is positive = 4/5
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cos%28B%29+=+4sqrt%2897%29%2F97

sub in Q4 is negative
sin(B) = -9sqrt(97)/97
---
sin(A+B) = sin(A)cos(B) + sin(B)cos(A)
= (3/5)*4sqrt(97)/97 - (9*sqrt(97)/97)*(4/5)
= 12sqrt(97)/(97*5) - 36sqrt(97)/97)/(97*5)
= -24sqrt(97)/485
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These problems are tedious and it's easy to make a mistake.
I'll check this tomorrow.
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All these are similar.
Look at "half angle formulas" on Wikipedia, it's covered well there.
Try them and email me via the TY note for help, or to check your work.
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2 cos(a+b)
3 sin (a-b)
4 cos(a-b)