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The problem:

Evaluate the inv. function by sketching a unit circ., finding the angle, and eval. the correct pair on the circle. Function: $\tan^{-1}(-1)$

I found a solution for this, but my teacher told me he'd prefer that I draw my conclusion by drawing the tan on the unit circle. I'm just not sure how I can deduce anything from that.

What I did was, that:

We know that $\tan^{-1}(-1)$ is the angle $\theta$ for which $\tan\theta = -1$. We know that $\tan\theta = \frac{\sin\theta}{\cos\theta} = 1$ when $\sin\theta = \cos\theta$.

That happens in the middle of each quadrant of the circle, I know this.. and that we therefore get $\tan\theta = -1$ in $-\frac{\pi}{4}$.

But how can I deduce this from drawing the tan line on the unit circle?

user2451412
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  • $\tan\theta=\frac{\sin\theta}{\cos\theta}=1$ is wrong. Because $\theta=\tan^{-1}(-1)$, the equation should be $$\frac{\sin\theta}{\cos\theta}=-1$$ $$\sin\theta= -\cos\theta$$Which quadrants are in the Domain of $\tan^{-1}$? – John Joy Aug 29 '14 at 20:34

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