# Solve equation tanx=3sinx

• Dec 13th 2009, 09:46 AM
aceband
Solve equation tanx=3sinx
Hi just worked through this question:

Solve the equation:
$tan(x) = 3sin(x)$

for $-180 < 0 < 180$

I get cos(x) = 1/3

and x = +- 70.5

The answer says it's also +- 180 which makes sense but i wondered how this second result can be found?

Thanks
• Dec 13th 2009, 09:56 AM
e^(i*pi)
Quote:

Originally Posted by aceband
Hi just worked through this question:

Solve the equation:
$tan(x) = 3sin(x)$

for $-180 < 0 < 180$

I get cos(x) = 1/3

and x = +- 70.5

The answer says it's also +- 180 which makes sense but i wondered how this second result can be found?

Thanks

EDIT: Does your book also give x=0 as a solution?

As you have written it you are right but the book's answer suggest your limits are actually $-180 \leq x \leq 180$. This means $\pm 180^o$ are allowable

You are cancelling out sin(x) in the second step which is potentially equal to 0. Instead, solve this equation via factorising.

$\frac{sin(x)}{cos(x)} = 3sin(x)$

$\frac{sin(x)-3sin(x)cos(x)}{cos(x)}=0$

$sin(x)(1-3cos(x))=0$

Either: $sin(x)=0$ (which is where -180,0,180 comes from)

or $cos(x)=\frac{1}{3}$ which you did

It is also interesting to note that this equation has a vertical asymptote at $x= \pm 90^o$