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.
