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effort
Senior Member

USA
38 Posts

Posted - 05/16/2013 :  13:50:32  Show Profile  Reply with Quote
Given cos= -7/9 and tan < 0, find 2

The 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.
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effort
Senior Member

USA
38 Posts

Posted - 05/16/2013 :  19:16:58  Show Profile  Reply with Quote
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 1
Using the pythagorean thm, I found the third side side to be 42.
So now, sin 2 = (42)/9 so sin = (82)/9


Solution 2
But 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)/9


So i don't understand why I can't solve it like my top????
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the_hill1962
Advanced Member

USA
1470 Posts

Posted - 05/17/2013 :  08:48:10  Show Profile  Reply with Quote
In your Solution1, sin 2 is not equal to (42)/9
That 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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