# simple trig

• Apr 13th 2009, 07:35 AM
djmccabie
simple 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, 07:40 AM
djmccabie
do i just divide sin and cos for tan?
• Apr 13th 2009, 08:08 AM
Hello djmccabie
Quote:

Originally Posted by djmccabie
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

Quote:

Originally Posted by djmccabie
do i just divide sin and cos for tan?

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

$2\sin a = 3\cos a$

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

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

$\Rightarrow \tan a = 1.5$

• Apr 13th 2009, 08:09 AM
masters
Quote:

Originally Posted by djmccabie
do i just divide sin and cos for tan?

Hi dj,

Yep, pretty much.

$2 \sin a = 3 \cos a$

$\frac{\sin a}{\cos a}=\frac{3}{2}$

$\tan a = \frac{3}{2}$

Now, can you find the two angles that satisfy the original equation?