Understanding the Tangent Function

The video tutorial explains how to graph the tangent function using the unit circle and reciprocal identity. It covers setting up the coordinate plane, identifying key angles, and calculating function values. The tutorial also discusses vertical asymptotes and provides a method to sketch the tangent graph on the interval from -π/2 to +π/2.

What is the reciprocal identity for tangent theta?

• Cosine theta divided by sine theta

• Sine theta multiplied by cosine theta

• Sine theta divided by cosine theta

• Cosine theta minus sine theta

What is the interval used for graphing the tangent function in this tutorial?

• 0 to 2π

• -π/2 to π/2

• -π to π

• 0 to π

How is the interval from -π/2 to π/2 divided for graphing purposes?

• Into four equal parts

• Into five equal parts

• Into three equal parts

• Into two equal parts

What is the tangent value at 0 radians?

• -1

• 0

• 1

• Undefined

At π/4 radians, what is the value of tangent theta?

• Undefined

• -1

• 1

• 0

What happens to the tangent function at π/2 radians?

• It is undefined

• It equals 0

• It equals 1

• It equals -1

Where do vertical asymptotes occur for the tangent function in this interval?

• At 0 radians

• At π/4 and -π/4 radians

• At π radians

• At π/2 and -π/2 radians

What is the significance of vertical asymptotes in the tangent graph?

• They indicate where the function is undefined

• They indicate minimum values

• They indicate maximum values

• They indicate where the function is zero

How can additional points be determined for the tangent graph?

• By using the same angles repeatedly

• By using only the key angles

• By using different angles and calculating Y divided by X

• By guessing the values

What is a useful way to remember the graph of the tangent function?

• By memorizing the sine function

• By using a calculator

• By knowing the unit circle

• By memorizing the cosine function