# Unit 5 – Graphs of the other Trigonometric Functions - PowerPoint PPT Presentation

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Unit 5 – Graphs of the other Trigonometric Functions. Warm Up 1-9 on the trig graphs review page done. Tangent and Cotangent. MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

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Unit 5 – Graphs of the other Trigonometric Functions

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## Unit 5 – Graphs of the other Trigonometric Functions

Warm Up

1-9 on the trig graphs

review page done

Tangent and Cotangent

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### In this section, you will learn to:

• Sketch the graphs of tangent and cotangent functions (Thursday/Friday)

• Sketch the graphs of secant and cosecant functions (Monday/Tuesday)

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the tangent curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the tangent curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the cotangent curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the cotangent curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

Question: Is there an amplitude for a tangent or a cotangent function? Why or why not?

No amplitude, since the two curves extend infinitely in both directions.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Period of Tangent and Cotangent Functions:

THIS IS DIFFERENT

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Asymptotes of the tangent graph function:

• Where do you think you need to set the left and right endpoints for a tangent graph below?

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Asymptotes of the tangent graph function:

Asymptotes for a tangent function can be found

by solving for the two equations:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Find the asymptotes of

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Find the asymptotes of

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Asymptotes of the cotangent graph function:

• Where do you think you need to set the left and right endpoints for a cotangent graph below?

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Asymptotes of the cotangent graph function:

Asymptotes for a cotangent function can be found

by solving for the two equations:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Find the asymptotes of

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Find the asymptotes of

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Reflection:

• If a is positive, then there is no reflection about the x-axis.

• If a is negative, then there is a reflection about the x-axis.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Effects of a on the tangent and cotangent graphs:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Effects of a on the tangent and cotangent graphs:

a) If a > 1, then the graph rises faster.

b) If 0< a < 1, then the graph rises slower.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Effects of c on the tangent and cotangent graphs:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Horizontal Translation or Phase Shift:

The constant c determines the phase shift of the graph.

Phase Shift = - c/b (or –c/b)

a) If c is positive, then the shift is toward the left.

b) If c is negative, then the shift is toward the right.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Effects of d on the tangent and cotangent graphs:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Vertical Translation:

The constant d determines the vertical

translation of the graph.

a) If d is positive, then the vertical shift is upward.

b) If d is negative, then the vertical shift is downward.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Find the amplitude, period, reflections, horizontal shift, vertical shift, endpoints and sketch the graph.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

a) Amplitude:

b) Period:

c) Horizontal Translation:

d) Vertical Shift:

e) Reflection:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

e) Endpoints:

Verify distance with the period:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the secant curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the secant curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the cosecant curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### The graph of the cosecant curve:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

• Is there an amplitude for a secant or a cosecant function? Why or why not?

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

• Period is

• The horizontal translation, vertical translation, and reflection all stay the same.

• It is best to sketch the cosecant and secant graph by first graphing the reciprocal functions of sine and cosine.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Find the amplitude, period, reflections, horizontal shift, vertical shift, endpoints and sketch the graph.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

a) Amplitude:

b) Period:

c) Horizontal Translation:

d) Vertical Shift:

e) Reflection:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

e) Endpoints:

Verify distance with the period:

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### Reflection:

• If a is positive, then there is no reflection about the x-axis.

• If a is negative, then there is a reflection about the x-axis.

• If b is positive, then there is no reflection about the y-axis.

• If b is negative, then there is a reflection about the y-axis.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

### HOMEWORK

• Graphing Trig Functions

• Kuta

• Trig graphs review page 1 and 2