# Ch 4  Graphs of the Circular Functions

## Ch 4.1  Graphs of the Sine and Cosine Functions

Graphing the Sine and Cosine Function

Finding the Period of y=cos(3x), and y=sin(x/4 );

Finding and Graphing the Amplitude and Period of  y=sin( x/3), y= 1/2 cos(2x) and y= –2sin(3x)

Finding the Amplitude and Period of y= –4cos(3x), y=1/2 sin(x) and y= √2 cos(1/2 x)

Describing the Transformation of y= –3cos(6x)

Graphing y = –2 cos(2x)

## Ch 4.2  Translations of the Graphs of the Sine and Cosine Functions

Graphing Phase Shifts (Horizontal Translation) for y=cos(x–4), y=sin[2(x+1)], and y=cos(10x+30)

Determining Which Graph Most Closely Resembles the Graph of y= –2sin(x–π)

Graphing Vertical Translation of y=sin (x)+1 and y=cos(x)–1/2;

Graphing Horizontal and Vertical Translation for y=sin(x– ╥/4)+1, and y= – 1/2 +cos(x+ ╥/2)

Graphing Horizontal and Vertical Translation for y=1/2+sin(x+ ╥/4)

Graphing Sine and Cosine with Different Coefficients (Amplitude, period, and Vertical Translation) : y=2sin(1/2 ╥x )–1

Graphing Sine and Cosine with Different Coefficients (Amplitude, period, Horizontal Translation, and Vertical Translation) :

y=4cos(4x–8)–1

Graphing y=2sin[2 (x+ ╥/4)]–1
y=1/2 cos(1/2 x– ╥/4)+2
y=4–sin [π(x+1)]

y=2cos (x– ╥/2)+1

Example: Describe the Transformations of Cosine Function from a Graph : Fill Out Amplitude, Period, Horizontal Transformation (Phase Shift), Vertical Transformation (Vertical Shift), Midline

## Ch 4.3  Graphs of the Tangent of Cotangent Functions

Graphing the Tangent Function y=tan θ

Example: Graphing the Tangent Function y=tan θ
Using the Unit Circle and the Reciprocal Identity tan θ=(sin θ/cos θ)

Graphing the Cotangent Function y=cot θ

Graphing Tangent and over a Different Period y=tan(4x)

Graphing Tangent and Cotangent over Different Periods and Amplitude :

y=tan(3x)
y=cot( x/4)
y=2tan(x/2 )
y=1/2 cot(2x)

y=cot(πx)
y=2cot(πx)

Graphing y=2cot(1/4 x) with Transformation

Identifying a Trigonometric a Function from Its Graph

## Ch 4.4  Graphs of the Secant and Cosecant Functions

Graphing y=csc θ Using y=sin θ
Graphing y=sec θ Using y=cos θ

Graphing y= –csc θ Using y=sin θ

Graphing a Transformation of Cosecant Function
y=2csc(2πx+π)+3

Example: Determine the Domain of the Secant and Cosecant Functions Using the Unit Circle