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Graphing Cosecant and Secant

Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = - –X max = 3 –X scale = /6 Window—

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Page 1: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing Cosecant and Secant

Page 2: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Using the Graphing CalculatorMode—

RadiansFunctionSequential

• Window—– X min = - – X max = 3– X scale = /6

• Window—– Y min =-5– Y max = 5– Y scale = .5

Page 3: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Press Y=y1 = sin (x)

y2 = 1/sin (x)

Press Graph

Page 4: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Press Y=y1 = 3sin (X)

y2 = 3/sin(x)

Press Graph

Page 5: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Press Y=y1 = sin (X) + 1

y2 = 1/sin (X) +1

Press Graph

Page 6: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Press Y=y1 = sin (x + 1)

y2 = 1/sin (x +1)

Press Graph

Page 7: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Press Y=y1 = sin (2x)

y2 = 1/sin (2x)

Press Graph

Page 8: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

What are you noticing???•The only points that the two curves have in common are the maxima and minima of the sine curve.

•The cosecant curve has asymptotes at the intercepts of the sine curve.

•The cosecant curve is just a series of “parabola shaped” graphs that alternate opening up and then down.

Page 9: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

What do you think the secant curve will look like?•Check out your thoughts by …

Press Y=y1 = cos (x)

y2 = 1/cos (x)

Page 10: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

So, let’s graph cosecant and

secant graphs.

Page 11: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing Cosecant Curve y = csc (x)

0

/6

/4

/3

/2

2/3

3/4

5/6

7/6

5/4

4/3

3/2

5/3

7/4

11/6

2

Page 12: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing Cosine Curvey =sec(x)

0

/6

/4

/3

/2

2/3

3/4

5/6

7/6

5/4

4/3

3/2

5/3

7/4

11/6

2

Page 13: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

So, let’s graph cosecant and secant graphs

with key points.

Page 14: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = 2 csc x Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(0, )(/2, )

(, )

(3/2, )

(2, )

Page 15: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = -2 sec x Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(0, )(/2, )

(, )

(3/2, )

(2, )

Page 16: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = sec 4x Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(0, )(/8, )

(/4, )

(3/8, )

(/2, )

Page 17: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = 3 csc 1/2x Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = _____

(0, )(, )

(2, )

(3, )

(4, )

Page 18: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = 3 sec x +2 Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(0, )(/2 )

(, )

(3/2, )

(2, )

Page 19: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = sec x +2 Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(0, )(/2 )

(, )

(3/2, )

(2, )

Page 20: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = csc (x + ) Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(-, )(-/2 )

(0, )

(/2, )

(, )

Page 21: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = sec (x - /4) Think: ____________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(/4 , )(3/4, )

(5/4, )

(7/4, )

(9/4, )

Page 22: Graphing Cosecant and Secant. Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -  –X max = 3  –X scale =  /6 Window—

Graphing by Key Pointsy = 2 sec (x/2 - /2) -1 Think: ________________

Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________

Inc. = ______

(, )(2, )

(3, )

(4, )

(5, )