# Solving Trig equations

• Aug 30th 2013, 09:30 PM
curt26
Solving Trig equations
Solve for x: tan(3x)=-1 , 0≤x≤180

I worked it out and I found x=7π/12. Because 7π/12 is out of the 0≤x≤180 interval, would that be my final answer?

Thanks
• Aug 30th 2013, 10:04 PM
curt26
Re: Solving Trig equations
Does the 3 call for me to increase my interval by 3 times making it 0≤x≤540 ?
• Aug 31st 2013, 01:57 AM
ibdutt
Re: Solving Trig equations
tan ( 3x ) = -1 = tan ( pi - pi/4 ) = tan ( 3pi/4 ) that gives 3x = 3pi/4 and so x = pi/4
also tan ( 3x ) = -1 = tan ( 2pi - pi/4 ) = tan ( 7pi/4 ) this implies 3x = 7pi/4 thus x = 7pi/12
Now you can draw the correct conclusion
• Aug 31st 2013, 06:20 AM
curt26
Re: Solving Trig equations
So the correct answer would be x=pi/4 because x=7pi/12 is not within the specified interval of 0≤x≤180?
• Sep 5th 2013, 02:19 PM
Re: Solving Trig equations
Hi Curt26,

Quote:

Originally Posted by curt26
Does the 3 call for me to increase my interval by 3 times making it 0≤x≤540 ?

No.

question specifically mentions your domain of x.

its not possible to change the domain.

the only difference that 3x does is to make you include some more values of x

Quote:

Originally Posted by curt26
So the correct answer would be x=pi/4 because x=7pi/12 is not within the specified interval of 0≤x≤180?

pi= 180 degrees

what's the value of 7pi/12

--------------------------

dont be afraid to have multiple answers.

x can have multiple values.

Cheers
• Sep 5th 2013, 04:58 PM
Soroban
Re: Solving Trig equations
Hello, curt26!

Quote:

$\displaystyle \text{Solve: }\:\tan(3x)\,=\,\text{-}1\qquad 0 \le x\le \pi$

$\displaystyle \text{Does the "3" call for me to increase my interval making it }0 \le {\color{red}3}x \le 3\pi\,? \;\;\;\color{blue}{\text{Yes!}}$

We have: .$\displaystyle \tan(3x) \:=\:\text{-}1$

Then: .$\displaystyle 3x \:=\:\frac{3\pi}{4},\;\frac{7\pi}{4},\;\frac{11\pi }{4}$

Therefore: .$\displaystyle x \;=\;\frac{\pi}{4},\;\frac{7\pi}{12},\;\frac{11\pi }{12}$