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# How to solve tan(x)= -1

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As stated in title

Guest Oct 18, 2017
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#1
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First, note that $$\tan({\pi\over4})=1$$. Imagine this on the unit circle. Since we need to find $$x$$ when its tangent is negative 1, we have to get to the 2nd and 4th quadrant while retaining the tangent's absolute slope. To do that, we add $$90^o$$ or $${\pi\over2}$$ and $$270^o$$ or $${3\pi\over2}$$ to the angle $${\pi\over4}$$. When we do that, we get the angles $${3\pi\over4}$$ and $${7\pi\over4}$$.

Q.E.D.

Mathhemathh  Oct 18, 2017
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That is a good answer mathhemathh

but QED means 'it is proven' so it is only appropriate to use it at the end of proofs

Melody  Oct 18, 2017
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Malis verbis meis...

Mathhemathh  Oct 18, 2017
#3
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tan(x) = -1        $$x=\frac{3}{4}\pi + k*\pi$$           $$k\epsilon Z$$

Omi67  Oct 18, 2017

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