3.8 AP The Tangent Function

Multiple Choice

Do not use an already-completed unit circle. Try it from memory or draw a new one.

$$\tan\left(\frac{\pi}{6}\right)=$$

• 2√3/3

• 2√3

• √3/3

• √3

Multiple Choice

$$\tan\left(\frac{7\pi}{4}\right)=$$

• 1

• -1

• √2

• • - √2

Multiple Choice

$$\tan\left(\frac{3\pi}{2}\right)=$$

• • undefined

• 0

• 1

• • - 1

Multiple Choice

$$\tan\left(\frac{\pi}{3}\right)=$$

• 2√3/3

• √3/3

• √3

• • 2√3

Multiple Choice

$$\tan\left(\frac{\pi}{4}\right)=$$

• 1

• -1

• √2

• • - √2

Multiple Choice

$$\tan\left(\pi\right)=$$

• • undefined

• 0

• 1

• • - 1

Multiple Choice

$$\tan\left(\frac{4\pi}{3}\right)=$$

• • - √3/3

• √3/3

• √3

• • - √3

Multiple Choice

$$\tan\left(\frac{5\pi}{6}\right)=$$

• • - √3/3

• √3/3

• √3

• • - √3

Multiple Choice

$$\tan\left(\frac{\pi}{2}\right)=$$

• • undefined

• 0

• 1

• • - 1

Multiple Select

Select all expressions that are equivalent to tanθ.

• x/y

• cosθ/sinθ

• sinθ/cosθ

• y/x

Multiple Choice

Select the formula for the slope of a line containing the points (x₁, y₁) and (x₂, y₂).

• $$\frac{x_2-y_1}{y_2-x_1}$$

• $$\frac{y_2-x_1}{x_2-y_1}$$

• $$\frac{x_2-x_1}{y_2-y_1}$$

• $$\frac{y_2-y_1}{x_2-x_1}$$

The tangent of an angle is the slope of the terminal ray.

• A terminal ray intersects the unit circle in the images above.

• At 0 radians (first image), the slope of the terminal ray is equal to tangent of 0 radians: y/x = 0/1 = 0.

• As we rotate counter-clockwise, the slope of the terminal ray increases (gets steeper) from 0 to π/2.
  

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Multiple Choice

Over the interval 0<θ<π/2, values of tanθ are

• increasing

• decreasing

• The slope of a vertical line is undefined.

• When θ=π/2, the slope of the terminal ray is equal to tangent of π/2: undefined.

• From π/2 to π, the slope of the terminal ray is now negative.

• As the terminal ray gets closer to π, the slopes become less negative, which means the slopes are still increasing.

• At π radians (last image), the slope of the terminal ray is equal to 0 again.

Multiple Choice

Over the interval π/2<θ<π, values of tanθ are

• increasing

• decreasing

Multiple Select

Select the angles where tangent is undefined. Select all that apply.

• 0

• π/2

• π

• 3π/2

• 2π

Multiple Select

Select the angles where tangent is 0. Select all that apply.

• 0

• π/2

• π

• 3π/2

• 2π

• The graph of y=tanx is pictured above.

• The angles where tangent is equal to 0 are the x-intercepts.

• The angles where tangent is undefined are vertical asymptotes.

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Multiple Select

Select the angle(s) where the graph of y=tanx has a vertical asymptote.

• 0

• π/2

• π

• 3π/2

• 2π

Multiple Select

Select all angle(s) where the graph of y=tanx has an x-intercept.

• 0

• π/2

• π

• 3π/2

• 2π