5.6 – Sketching the Basic Trigonometric Functions Using the chart ...
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5.6 – Sketching the Basic Trigonometric Functions. Using the chart (table of
values) that is generated from the “Unit Circle” one can plot and sketch the basic
...
5.6 – Sketching the Basic Trigonometric Functions Using the chart (table of values) that is generated from the “Unit Circle” one can plot and sketch the basic trigonometric functions (see following investigation sheet); f(x) = sin θ Rough sketch as amplitude is changed
g(x) = cos θ
h(x) = tan θ
10
10
10
5
5
5
−π
π
2π
3π
4π
−π
π
2π
3π
4π
−π
π
−5
−5
−5
−10
−10
−10
2π
3π
4π
On graphing calculator you can change mode to DOT to see individual point and no asymptote
The “unit circle” provided values for one rotation (0° ≤ θ ≤ 360°) but one could keep rotating the radial arm to generated a repeating pattern for any angle. In Degrees
Rough sketch using y = sin x
In Radians 10
8 6
5
4 2 −180
180
−2
360
540
720
−π
−4
π
2π
3π
4π
−5
−6 −8
−10
10
This generates a Periodic Function, which is defined as pattern of y-values that repeat at regular intervals. Some specific terminology associated with periodic behavior is outlined below. Cycle describes one complete pattern (end up at the same y-value that started with) Period describes the horizontal length (x-length) of one cycle Amplitude is half the distance between the maximum (peak) and minimum (trough) values of the function. Amplitude = (max-min)/2 Average is the middle between max and min of the function. Average = Min + Amplitude 1 cycle
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