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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 (A-B) 2) Sin (A+B) 3) cos (A+B) 4) tan (A-B) 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‰ˇ sin(A)cos(B) - cos(A)sin(B) = -(4/5)(8/17) - (3/5)(15/17) = -77/85. 2) sin(A + B) â‰ˇ 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‰ˇ 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. Tags expression, finding, trigonometric, values ,

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evaluate the expression given that cos a=4/5 with 0

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