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(1) Trigonometry 5

# (1) Trigonometry 5 - Pre Calculus Math 40S Explained...

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Pre – Calculus Math 40S: Explained! www.math40s.com 43 TRIGONOMETRY LESSON FIVE PART I - PERIOD The period of a graph is defined as the length of one complete cycle. This graph has a period of 2 π This graph has a period of 4 π This graph has a period of π Most graphs given to you won’t be as simple as the first three. In trig graphs that are continuous, you will have to first identify a sine or cosine pattern before you can determine the period. The easiest way to do this is to draw a square around either pattern and look at the length. The graph on the left has a period of π
Pre – Calculus Math 40S: Explained! www.math40s.com 44 TRIGONOMETRY LESSON FIVE PART I - PERIOD Questions: For each of the following graphs, draw a rectangle around the indicated pattern and state the period. 1) Draw a rectangle around a sine pattern. 2) Draw a rectangle around a cosine pattern. 3) Draw a rectangle around a sine pattern. 4) Draw a rectangle around a sine pattern. 5) Draw a rectangle around a sine pattern. 6) Draw a rectangle around a cosine pattern.

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Pre – Calculus Math 40S: Explained! www.math40s.com 45 TRIGONOMETRY LESSON FIVE PART I - PERIOD ANSWERS: 1) Period = 8 π 2) Period = 4 π 3) Period = 4 π 4) Period = π 3 5) Period = π 6) Period = π 2 3
Pre – Calculus Math 40S: Explained! www.math40s.com 46 TRIGONOMETRY LESSON FIVE PART II - THE B VALUE The “b” value represents the number of cycles a trig graph has within a span of 2 π . It is the number that you see in a trig function right beside θ . (y = sinb θ ) The b value is NOT the period. The b-value and period (for radians) are related by the formula: π π 2 2 Pe riod = b = b Period or The b-value and period (for degrees) are related by the formula: D D 360 360 P eriod = b = b Period or Example 1: Draw the graph of y = sin2 θ θ π (0 2 ) The first step in graphing this trig function is to find the period. Once we know the period, draw the graph from 0 to 2 π , since that is the specified domain. Note that tan θ graphs do not use these equations for the period and b-value. 2 Period = b 2 π Period = 2 Period = π π 1 2 θ θ π (0 ) ≤ 4 Example 2: Draw the graph of y = cos The first step in graphing this trig function is to find the period. Once we know the period, draw the graph from 0 to 4 π since that is the specified domain.

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(1) Trigonometry 5 - Pre Calculus Math 40S Explained...

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