Which points are on the graph of y=tan x? Select all that apply. (2 answers)
a. [4pi/3, sqrt(3)]***
b. [pi/4, -1]
c. [pi/6, -sqrt(3)/3]
d. [pi/3, sqrt(3)]***
e. [1, -pi/4]
To determine which points are on the graph of y = tan x, we can substitute the x-values into the equation and check if the resulting y-values match.
a. [4pi/3, sqrt(3)]: Substitute x = 4pi/3 into y = tan(x):
tan(4pi/3) = sqrt(3)
This point is on the graph of y = tan x.
b. [pi/4, -1]: Substitute x = pi/4 into y = tan(x):
tan(pi/4) = 1
This point is not on the graph of y = tan x.
c. [pi/6, -sqrt(3)/3]: Substitute x = pi/6 into y = tan(x):
tan(pi/6) = 1/√3 = √3/3
This point is not on the graph of y = tan x.
d. [pi/3, sqrt(3)]: Substitute x = pi/3 into y = tan(x):
tan(pi/3) = √3
This point is on the graph of y = tan x.
e. [1, -pi/4]: Substitute x = 1 into y = tan(x):
tan(1) is not a simple fraction or a commonly known value.
This point is not on the graph of y = tan x.
Therefore, the points that are on the graph of y = tan x are [4pi/3, sqrt(3)] and [pi/3, sqrt(3)].
To determine which points are on the graph of y = tan x, we need to substitute the x-values into the equation and check if the y-values match.
Let's go through each option:
a. [4π/3, √3]: To check if this point is on the graph, substitute x = 4π/3 into the equation.
y = tan(4π/3) ≈ 1.732
The y-value does not match √3, so this point is not on the graph.
b. [π/4, -1]: To check if this point is on the graph, substitute x = π/4 into the equation.
y = tan(π/4) = 1
The y-value does not match -1, so this point is not on the graph.
c. [π/6, -√3/3]: To check if this point is on the graph, substitute x = π/6 into the equation.
y = tan(π/6) = 1/√3 ≈ 0.577
The y-value does not match -√3/3, so this point is not on the graph.
d. [π/3, √3]: To check if this point is on the graph, substitute x = π/3 into the equation.
y = tan(π/3) ≈ 1.732
The y-value matches √3, so this point is on the graph.
e. [1, -π/4]: To check if this point is on the graph, substitute x = 1 into the equation.
y = tan(1) ≈ 1.557
The y-value does not match -π/4, so this point is not on the graph.
Based on our analysis, only option d. [π/3, √3] is on the graph of y = tan x. Therefore, the correct answers are d. [π/3, √3].