3.8 The Tangent Function

What is the fundamental period of y = tan(x)?

• π/4

• π

• π/2

• 2π

• 2

Vertical asymptotes of y = tan(x) occur at which x-values?

• x = π/4 + πk

• x = π/3 + 2πk

• x = 2πk

• x = π/2 + πk

• x = πk

For h(x) = 7 − 3 tan(4x), what is the period of h?

• 4π

• π

• 2π

• π/2

• π/4

If h(θ) = cot(2θ), the vertical asymptotes of its graph occur at which θ-values?

• θ = π/2 + πk

• θ = π + 2πk

• θ = π/2 k

• θ = πk

• θ = π/2 + πk

The graph of f(x) = a tan(bx) is reflected across the x-axis and has period π/2. Which combination must be true?

• a = 0 and b > 1

• a < 0 and b < 1

• a < 0 and b > 1

• a > 0 and 0 < b < 1

• a > 0 and b > 1

In the xy-plane, an angle θ is in standard position and the slope of its terminal ray equals tan(θ). If the slope is -1, which could be a measure of θ?

• 3π/4

• π/4

• 5π/6

• 11π/6

In standard position, an angle θ has terminal ray with slope undefined. Which angle measure fits?

• π

• 3π/4

• π/2

• π/6

What is the slope of the terminal ray for an angle θ = π/3 in standard position?

• √3

• 1

• 1/√3

• 0

• 2

Evaluate tan(3π/4).

• −1

• −√3

• 1

• 0

• √3

Evaluate tan(11π/6).

• √3

• −√3

• 0

• −1/√3

• 1/√3