Module 21 - Graphs of Trigonometric Functions

What is the phase shift of y = tan[2x+(∏/6)]?

-∏/12

What is the phase shift of y = tan[(1/2)x-(∏/3)]?

2∏/3

What is the phase shift of y = sin[(1/3)x-(3∏/2)]?

9∏/2

What is the definition of phase shift?

A phase shift is the horizontal translation of a periodic function.

What is the domain, range, x and y-intercepts of tan?

The domain is all reals except integers of ∏ and 0. The range is (-∞, ∞). The x-intercepts are odd integers of ∏/2. There are no y-intercepts.

What is the domain, range, x and y-intercepts of cot?

The domain is all reals except odd integers of ∏/2. The range is (-∞, ∞). The x-intercepts are integers of ∏ and 0. There are no y-intercepts.

What is the domain, range, x and y-intercepts of cos?

The domain of cos is (-∞, ∞). The range of cos is [-1, 1]. The x-intercepts of cos are on odd integers of ∏ and 0. The y-intercept of cos is (0, 1)

What is the domain, range, x and y-intercepts of sin?

The domain of sin is (-∞, ∞). The range of sin is [-1, 1]. The x-intercepts of sin are on even integers of 2∏ and 0. The y-intercept of sin is (0, 0)

What is the period and amplitude of y = sin(x) and y = cos(x)?

The period is 2∏ and the amplitude is 1.

What is the period and amplitude of y = tan(x) and y = cot(x)?

The period is ∏ and the amplitude does not exist because the range of tan and cot is infinite.

What is the periodicity, amplitude, domain, range, x and y-intercepts of csc?

The periodicity is even integers of 2∏. The amplitude does not exist. The domain is all reals except even integers of 2∏ and 0. The range is (-∞, -1) ∪ (1, ∞). Cos has no x-intercepts. Cos has no y-intercepts.

What is the periodicity, amplitude, domain, range, x and y-intercepts of sec?

The periodicity is odd integers of ∏. The amplitude does not exist. The domain is all reals except odd integers of ∏. The range is (-∞, -1) ∪ (1, ∞). Sec has no x-intercepts. The y-intercept is at (0, 1).

What is the phase shift and amplitude of y = 2cos[3x-(∏/2)]?

The phase shift is ∏/6. The amplitude is 2.