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 = asinxy = acosx The amplitude will stretch the graph vertically. The value of “a” is half the distance of the max and min.

Amplitude “a” Graph y = 3cosx

Period of the sine and cosine y = 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.

Period of the sine and cosine Graph y = sin3x

Period of the sine and cosine Graph y = cos2x

Amplitude “a” and Period ”b” Graph y = 3sin4x

Amplitude “a” and Period ”b” Graph y = -4cosπx

Phase Shifts of sine and cosine y = 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

Phase Shifts of sine and cosine Graph

Phase Shifts of sine and cosine Graph

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

Vertical Translations of sine and cosine Graph y = 2 + sinx

Vertical Translations of sine and cosine Graph y = -2 + cos3x

Graph y = -2 – 2sin5x Combinations of Translations

Graph y = 1 -2cos3(x+π) Combinations of Translations

Graph

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

Graph y = secx Graphs of Secant and Cosecant

Graph y = cscx Graphs of Secant and Cosecant

Graph y = 2csc5x 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.

Over “2-periods” Graph y = sinx

Over “2-periods” Graph

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 = tanx

Tangent and Cotangent Graph y = cotx

Tangent and Cotangent Graph y = 1 – tan3x

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.

Graph y = 1 + tan(2x + π) Graph the following over 2 periods

Tangent and Cotangent Graph Period: π/2 Phase Shift: π/8 to the left Vertical Translation: up 1 Find the amplitude, period, phase shift, and vertical translation…then graph it. Amplitude: not applicable

Tangent and Cotangent Graph Find the amplitude, period, phase shift, and vertical translation…then graph it.

A chart for you

Write the equation of a graph given the following information. 1. A negative Cosine function, amplitude 2, period π, phase shift π/2 to the left, vertical translation down A positive Sine function, amplitude 1, period π/4, phase shift π to the right, vertical translation up A negative Tangent function, period π, phase shift π to the left, vertical translation down 1. Y = -2-2cos(2x + π) Y = 1 + sin(8x – 8π) Y = -1-tan(x + π)

Write the equation of a graph. Y = 2cos2x

Write the equation of a graph. or

Write the equation of a graph.

TEAMS p. 181…….#’s 17-22

Write an equation for one cycle of this tide graph. November 3 rd 2014

Write the equation for this graph: Y=secx

Write the equation for this graph: Y=1+2cos2x

Write the equation for this graph:

Ch4 HW #7