graphing trigonometric functions
DESCRIPTION
Graphing Trigonometric Functions. Chapter 4. The sine and cosine curves. Graph y = sinx. The sine and cosine curves. Graph y = cosx. The sine and cosine curves. Graph y = - cosx. The sine and cosine curves. Graph y = - sinx. Amplitude “a”. y = asinx y = acosx - PowerPoint PPT PresentationTRANSCRIPT
Amplitude “a”
y = asinx y = acosx
The amplitude will stretch the graph vertically. The value of “a” is half the distance of the max and min.
Period of the sine and cosiney = sinbx and y = cosbx
The period of the function will shrink or stretch the graph horizontally. The period of a function is
The standard period is 2π, this occurs when b = 1.
Phase Shifts of sine and cosiney = sinb(x-d) and y = cosb(x-d)
The period of the function will have new endpoints when solving the inequality 0 ≤ b(x-d) ≤ 2π.(x – d) is a shift of “d” to the right(x + d) is a shift of “d” to the left
Vertical Translations of sine and cosine
y = c + sinx and y = c + cosx
The “c” will shift the entire graph “c” units up when “c” is positive and “c” units down when “c” is negative
Identifying Features
Give the amplitude, period, phase shift, and vertical translation.
Amplitude: 2
Period: 2π
Phase Shift: π/3 to the left
Vertical Translation: none
Identifying Features
Give the amplitude, period, phase shift, and vertical translation.
Amplitude: 1
Period: 2π/3
Phase Shift: π/6 to the right
Vertical Translation: up 1
Identifying Features
Give the amplitude, period, phase shift, and vertical translation.
Amplitude: 4
Period: π
Phase Shift: π to the right
Vertical Translation: down 2
Graphs of Secant and Cosecant
Find the amplitude, period, phase shift, and vertical translation…then graph it.
Amplitude: not applicable
Period: π
Phase Shift: π/6 to the left
Vertical Translation: down 1
Graphs of Secant and Cosecant
Find the amplitude, period, phase shift, and vertical translation…then graph it.
Graphs of Secant and Cosecant
Find the amplitude, period, phase shift, and vertical translation…then graph it.
Amplitude: not applicable
Period: 2π
Phase Shift: π/4 to the right
Vertical Translation: up 2
Graphs of Secant and Cosecant
Find the amplitude, period, phase shift, and vertical translation…then graph it.
Tangent and Cotangent
• Sine,Cosine,Secant, and Cosecant have a standard period of 2π.• The tangent and cotangent have a standard period of π. • The standard tangent graph has asymptotes at –π/2 and π/2• The standard cotangent graph has asymptotes at 0 and π
Tangent and Cotangent
• Graph y = 2 + 3cot(x – π)
Amplitude: not applicable
Period: π
Phase Shift: π to the right
Vertical Translation: up 2
Find the amplitude, period, phase shift, and vertical translation…then graph it.
Tangent and Cotangent
• Graph y = 2 + 3cot(x – π)
Find the amplitude, period, phase shift, and vertical translation…then graph it.