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Find the exact value of each expression.

(a) $ \tan^{-1} \sqrt{3} $(b) $ \arctan (-1) $

a) $\frac{\pi}{3}$b) $-\frac{\pi}{4}$

01:01

Jeffrey P.

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

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when you see a phrase like this inverse tangent of square root three, here's what you want to think. What this is saying is find the angle. You're always finding an angle when doing inverse trig, Find the angle whose tangent is square root? Three. Okay, remember that when you're finding the angles, they have toe be between negative pi over two and positive pi over two for inverse tangent. So if it's positive square root three that we're looking at, then we would have an angle in quadrant one. We're finding that angle, and we know that it's opposite. Over adjacent is square root three. So we could think of that. A square root 3/1. Now what's the high pot news? Or do we even need to know? Do we recognize this right triangle? We should recognize it as a 30 60 90 triangle with legs of length one and square root three and high pot. News of length to that means we have a 60 degree reference angle there, so our angle is 60 degrees. Although we're not giving our answer and degrees, we're giving our answer and radiance, and that would be pi over three radiance. Okay. Similarly, if you see the expression arc tangent of negative one, here's what you want to think. This is asking you to find the angle whose tangent is negative? One. Remember, if it says inverse tangent or it says Arc tangent, it means the exact same thing. So the angle whose tangent is negative? One. That means we must be down in Quadrant four, since it's a negative. Negative one is the same as having negative one divided by one. So the opposite would be negative one and the adjacent would be one. And hopefully we recognize that as a 45 45 90 triangle with sides of length 11 and square root, too. So we know we have a 45 degree angle. Since we went clockwise, that would be considered negative 45 degrees and then converting that to radiance. We have negative pi over four radiance

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