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
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
Hi Curt26,
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
pi= 180 degrees
what's the value of 7pi/12
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dont be afraid to have multiple answers.
x can have multiple values.
Cheers
Hello, curt26!
$\displaystyle \text{Solve: }\:\tan(3x)\,=\,\text{-}1\qquad 0 \le x\le \pi$
$\displaystyle \text{Does the "3" call for me to increase my interval making it }0 \le {\color{red}3}x \le 3\pi\,? \;\;\;\color{blue}{\text{Yes!}}$
We have: .$\displaystyle \tan(3x) \:=\:\text{-}1$
Then: .$\displaystyle 3x \:=\:\frac{3\pi}{4},\;\frac{7\pi}{4},\;\frac{11\pi }{4}$
Therefore: .$\displaystyle x \;=\;\frac{\pi}{4},\;\frac{7\pi}{12},\;\frac{11\pi }{12}$