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May 12th, 2008, 01:37 PM  #1 
Newbie Joined: May 2008 Posts: 2 Thanks: 0  finding values for trigonometric expression
Can someone help me with this question? Determine the exact value for each trigonometric expression, given sinA= 4/5, cos B= (8/17), [(pi)/2] < A < pi and (pi) < B < [3(pi)/2] Find 1) sin (AB) 2) Sin (A+B) 3) cos (A+B) 4) tan (AB) if you could just tell me one of the answers and how you got to it, or even just help me get it started, i can probably figure out the rest. I just dont even know where to begin! thank youuuuuu!! 
May 12th, 2008, 01:39 PM  #2 
Newbie Joined: May 2008 Posts: 2 Thanks: 0  correction
all the < signs should be "less than or equal to" ..sorry!

May 13th, 2008, 02:14 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
You can use "<" instead of "â‰¤", as the values given for sin(A) and cos(B) are inconsistent with equality. sin(pi  A) = sin(A) = 4/5, so cos(A) = cos(pi  A) = 3/5 (by Pythagoras's theorem). cos(B  pi) = cos(B) = 8/17, so sin(B) = sin(B  pi) = 15/17 (by Pythagoras's theorem). 1) sin(A  B) â‰¡ sin(A)cos(B)  cos(A)sin(B) = (4/5)(8/17)  (3/5)(15/17) = 77/85. 2) sin(A + B) â‰¡ sin(A)cos(B) + cos(A)sin(B) = (4/5)(8/17) + (3/5)(15/17) = 13/85. (This is trigonometry, not calculus, so the topic will probably be moved from this section after a while.) 3) cos(A + B) â‰¡ cos(A)cos(B)  sin(A)sin(B) = (3/5)(8/17) + (4/5)(15/17) = 84/85. 4) tan(A  B) = sin(A  B)/cos(A  B) = (77/85)/(36/85) = 77/36. 

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expression, finding, trigonometric, values 
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