The point (π/4, 1) lies on the graph of y = tan x. Therefore, ...

Question

The point (π/4, 1) lies on the graph of y = tan x. Therefore, the point _______ lies on the graph of y = tan⁻¹ x.

Accepted Answer

Hello, everyone. We are asked to write the point that lies on the graph of Y equals the arc sine of X. If the point pi divided by 61 half lies on the graph of Y equals the sine of X, our answer choices are a, the 0.1 half pi divided by six B, the point negative one half negative pi divided by six, see the 0.1 half pi divided by three D, the point pi divided by six negative one half, all right. So let's start with what I know. So I know that I have Y equals the sine of X. And in this case, we know the point pi divided by 61 half is a solution. So this means that one half would equal the sign of pi divided by six. OK. So if we have the inverse, when we do the inverse, we do the opposite, we flip the X and the Y. So to get the equation, Y equals the sine of negative one X, we started with X equals the sign of Y and then we took the inverse sign of both sides. So that gets us the inverse sign of X equals Y. So if I do that on my original, the Y equals the sin of X, if I take the inverse sign of both sides, I find that the inverse sign or the arc sign of one half would equal pi divided by six. So this means if I match that up to the inverse formula, we were given where Y equals the inverse sign of X, we would get the 0.1 half pi divided by six. And that's our answer. So the point that lies on the graph of the inverse sign of X is the 0.1 half pi divided by six which is answer choice A have a nice day.

The point (π/4, 1) lies on the graph of y = tan x. Therefore, the point _______ lies on the graph of y = tan⁻¹ x.

Key Concepts

Inverse Trigonometric Functions

Function and Inverse Function Relationship

Properties of the Tangent Function

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