abelkoontz

How to recognize which double angle formula to use?

When they say given Sin B = 2/3

Find Cos B, How do you automatically know which double angle formula to use out of the ones given on the formula booklet 

 

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Well, you want cos B, not cos (2B), so of course you'll use the first one, which only requires you to know sin B.

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If Sin(B)=2/3, you also need to know in which quadrant B is in. Otherwise, you can have two possible answers. For this question, the double angle is not necessary to find cos(B). Just draw a right angle triangle with the opposite side of 2 and hypotenuse of 3 and use Pythagoras to find the last side. Once you have that, the adjacent to the hypoteneuse is the ratio you want for cos(B).

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In general it's all about practice. With more practice the more familiar you will be with the identities. You don't become automatic by memorizing any patterns. you become automatic after doing over 50 of such problems. 

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