Trigonometry Graphs



Trigonometry Graphs

To draw the graphs for sin, cos, and tan, you must use the quadrantal angles. For the tan curve you also need to remember that tan 45° = 1.

| |0 |90 |180 |270 |

|sin | | | | |

|cos | | | | |

|tan | | | | |

Steps to drawing the basic trig. graphs:

1) Count each box as 15°. So you count 6 boxes for each 90 degree interval (0-90, 90-180, 180-270, and 270-360).

2) Use the exact value from the quadrantal angle chart to plot your points on the graph.

3) After plotting the points on the graph, draw a smooth curve to connect the points. DO NOT DRAW STRAIGHT LINES!!!!!

4) Label your graph with the appropriate equation.

Example #1: Graph y = sin θ

[θ (theta) is sometimes used instead of x. You treat them the same.]

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Example #2: Graph y = cos θ

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Example #3: Graph y = tan θ

• Remember: When drawing the tan curve, you need to include that tan 45° = 1 in addition to the quadrantal angles.

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Amplitude and Period

y = A sin Bx

Amplitude: The height of the graph. In the above equation, the amplitude is controlled by “A” .

Example #4: Graph y = 2 sin θ

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Period: The time it takes to go through one cycle and then start over again. In the equation at the top of the page, the period is controlled by “B”.

Example #5: Graph y = sin 2θ (Since we changed “B” to 2, there will be 2 complete curves between 0° and 360°

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Practice:

1) y = 3 cos θ

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2) y = tan 3θ

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3) y = 4 sin 2θ

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