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effort
Senior Member

USA
38 Posts

 Posted - 05/16/2013 :  13:50:32 Given cos= -7/9 and tan < 0, find 2The answer in the book shows (-562) / 81 but that is not what I got. My answer is (82)/ 9 Am I just completely wrong or is the solution in the book? Any help is appreciated.

effort
Senior Member

USA
38 Posts

 Posted - 05/16/2013 :  19:16:58 Okay, here is my work. I have worked it twice. I have two answers. I don't understand why i can't solve it like the first solution.Solution 1Using the pythagorean thm, I found the third side side to be 42.So now, sin 2 = (42)/9 so sin = (82)/9Solution 2But if i use the sum formula for sin. I have sin( x + x) which equals sinxcosx + cosxsinx which equals (2)((42)/9)(-7/9) which equals what the books has for the solution (-562)/9So i don't understand why I can't solve it like my top????

the_hill1962

USA
1468 Posts

 Posted - 05/17/2013 :  08:48:10 In your Solution1, sin 2 is not equal to (42)/9That is what sin is equal to.So, since sin=(42)/9 and sin 2 = 2sincos, you get what you have done in the Solution2. Edited by - the_hill1962 on 05/17/2013 08:52:18
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