find all the values of a in the range 0 deg to 360 deg satisfying 2sina = 3cosa

i know its simple but just cant remember how to do it

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- Apr 13th 2009, 06:35 AMdjmccabiesimple trig
find all the values of a in the range 0 deg to 360 deg satisfying 2sina = 3cosa

i know its simple but just cant remember how to do it - Apr 13th 2009, 06:40 AMdjmccabie
do i just divide sin and cos for tan?

- Apr 13th 2009, 07:08 AMGrandad
Hello djmccabie

Yes, you do, but remember that you must make sure that what you're dividing by is not zero. So you need to say:

$\displaystyle 2\sin a = 3\cos a$

$\displaystyle \Rightarrow 2\tan a = 3$, provided $\displaystyle \cos a \ne 0$

Then check that $\displaystyle \cos a = 0$ does not give any valid solutions and proceed with

$\displaystyle \Rightarrow \tan a = 1.5$

Grandad - Apr 13th 2009, 07:09 AMmasters