Solving Tan x = -6 on [0, 2π]

The video tutorial explains how to solve the equation Tan x = -6 within the interval from 0 to 2π radians. It discusses the use of the inverse tangent function to isolate x and the necessity of using a calculator to find approximate solutions. The tutorial identifies two solutions within the specified interval, one in the fourth quadrant and another in the second quadrant, and verifies these solutions using a graph of the tangent function.

What is the equation we are trying to solve in this tutorial?

• Tan x = 6

• Tan x = -6

• Sin x = -6

• Cos x = 6

Why can't we find the tangent of -6 using the unit circle?

• Because the unit circle only shows positive values

• Because the unit circle is only for sine and cosine

• Because -6 is not a valid angle

• Because -6 is not a value on the unit circle

What is the domain of the inverse tangent function?

• Only positive numbers

• Only negative numbers

• Only integers

• All real numbers

What is the range of the inverse tangent function?

• -π/2 to π/2

• 0 to π

• -π to π

• 0 to 2π

What is the approximate value of x when using the calculator for Tan x = -6?

• -2.1456 radians

• 2.1456 radians

• -1.1456 radians

• 1.1456 radians

In which quadrant is the first solution for Tan x = -6 found?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

How do you calculate the first solution in the given interval?

• π plus the reference angle

• π minus the reference angle

• 2π plus the reference angle

• 2π minus the reference angle

In which quadrant is the second solution for Tan x = -6 found?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

How do you calculate the second solution in the given interval?

• π minus the reference angle

• π plus the reference angle

• 2π plus the reference angle

• 2π minus the reference angle

What method can be used to verify the solutions graphically?

• Graphing the inverse tangent function

• Graphing the tangent function and a horizontal line

• Graphing the cosine function

• Graphing the sine function