# How do you find Tan^-1(-1) without a calculator?

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Nov 5, 2015

The answer is $- \frac{\pi}{4}$

#### Explanation:

Alright, archtan / ${\tan}^{-} 1 \left(x\right)$ is the inverse of tangent. Tan is $\frac{\sin}{\cos}$. Like the inverse of sin, the inverse of tan is also restricted to quadrants 1 and 4.

Knowing this we are solving for the inverse of tan -1. We are basically being asked the question what angle/radian does tan(-1) equal. Using the unit circle we can see that tan(1)= pi/4.

Since the "Odds and Evens Identity" states that tan(-x) = -tan(x). Tan(-1)= -pi/4.

Knowing that tan is negative in quadrants 2 and 4. the answer is in either of those two quadrants. BUT!!! since inverse of tan is restricted to quadrants 1 and 4 we are left with the only answer -pi/4.

I am a college student taking Trig. please add any thing that could be wrong or added to benefit the answer. Hope this helped! :)

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