Evaluate the expression. tan − 1 1 \tan^{-1}1 tan − 1 1

this problem, we're asked to evaluate the expression the inverse tangent of 1. Now here we can also think of this as okay the tangent of what angle is going to be equal to 1 and we're trying to find the angle for which that is true. Now I know that my angle has to be in between negative pi over 2 and positive pi over 2 because that is our specified interval when working with the inverse tangent. And I also know that because this is a number, positive one, I am specifically looking in this first quadrant where all of my tangent values are positive. So for which value in this or for which angle in this first quadrant is the tangent positive 1? Well, for pi over 4, I see that my tangent is indeed 1, so that represents my solution, pi over 4 for the inverse tangent of 1. Thanks for watching and I'll see you in the next one.

Evaluate the expression. tan ⁡ − 1 1 \tan^{-1}1 tan − 1 1

− π 4 -\frac{\pi}{4} − 4 π

11. Inverse Trigonometric Functions and Basic Trig Equations

Inverse Sine, Cosine, & Tangent

Precalculus

11. Inverse Trigonometric Functions and Basic Trig Equations

Inverse Sine, Cosine, & Tangent

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Multiple Choice

Evaluate the expression.
$\tan^{-1}1$

$0$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$-\frac{\pi}{4}$

Verified step by step guidance

Understand that the expression involves the inverse tangent function, $ \tan^{-1} $, which is also known as $ \arctan $. This function returns the angle whose tangent is the given number.

Recognize that $ \tan^{-1}(1) $ asks for the angle whose tangent is 1. Recall that the tangent of $ \frac{\pi}{4} $ is 1, which is a key angle in trigonometry.

Consider the range of the $ \tan^{-1} $ function, which is $ (-\frac{\pi}{2}, \frac{\pi}{2}) $. This range helps determine the principal value of the angle.

Since $ \tan^{-1}(1) $ falls within the range and $ \tan(\frac{\pi}{4}) = 1 $, the angle that satisfies $ \tan^{-1}(1) $ is $ \frac{\pi}{4} $.

Verify the options given: $ \frac{\pi}{4} $, $ \frac{\pi}{2} $, and $ -\frac{\pi}{4} $. The correct angle that satisfies $ \tan^{-1}(1) $ is $ \frac{\pi}{4} $.