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13.4 – The Sine Function. I. Interpreting Sine Functions The sine function, y = sin θ, matches the measure θ of an angle in standard position with the.

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Presentation on theme: "13.4 – The Sine Function. I. Interpreting Sine Functions The sine function, y = sin θ, matches the measure θ of an angle in standard position with the."— Presentation transcript:

1 13.4 – The Sine Function

2 I. Interpreting Sine Functions The sine function, y = sin θ, matches the measure θ of an angle in standard position with the y – coordinate on the unit circle. The sine function, y = sin θ, matches the measure θ of an angle in standard position with the y – coordinate on the unit circle. The periodic sine function has one cycle every 360° or 2π The periodic sine function has one cycle every 360° or 2π –Hence the sine of any degree greater than 2π, then the cycle is repeated.

3 The x-axis or domain will be thought of in terms of theta, θ The x-axis or domain will be thought of in terms of theta, θ When graphing you have to pay attention to the domain of theta. Trig Cycles are repeated once every 360 degrees or 2π When graphing you have to pay attention to the domain of theta. Trig Cycles are repeated once every 360 degrees or 2π

4 The General Sine Curve:

5 Example 1: Graph, using a table the values of the sine curve in the domain Example 1: Graph, using a table the values of the sine curve in the domain 0 θ 2π. Use only the coordinates on the θ and y axes.

6 You can vary the period and amplitude of the sine curve to get different curves, either extended or more frequent You can vary the period and amplitude of the sine curve to get different curves, either extended or more frequent Done my multiplying the function by a constant, and theta by a constant Done my multiplying the function by a constant, and theta by a constant

7 Y = 3 sin θ

8 Y = sin 2θ

9 II. Properties of the Sine Function y = a sin bθ y = a sin bθ ІaІ = the amplitude (the highest and lowest points on the curves.) b = the number of cycles the curve makes from 0 to 2π 2π / b = the period of the cycle

10 Steps to Graphing y = a sin bθ Steps to Graphing y = a sin bθ –Step 1: draw your reference curve –Step 2: identify the domain and set up your graph. –Step 3: identify the amplitude and document –Step 4: identify the number of cycles in the domain that you have to graph –Step 4: identify the period you need to create one cycle –Step 5: Alter graph in needed in increments of 4 units on the theta axis to meet the criteria of the total cycles.

11 Example 2: how many cycles does the following have in the domain from 0 to 2π? Give the amplitude and period as well. Example 2: how many cycles does the following have in the domain from 0 to 2π? Give the amplitude and period as well. A) y = -5 sin 2θ B) f(x) =.5 sin.5θ

12 Example 3: Graph the following. (check on the calculator) Example 3: Graph the following. (check on the calculator) A) y = -2 sin 2θ, for 0 < θ < 2π A) y = -2 sin 2θ, for 0 < θ < 2π B) y = 5 sin θ, for 0 < θ < 2π B) y = 5 sin θ, for 0 < θ < 2π C) y = ½ sin.5θ, for 0 < θ < 2π C) y = ½ sin.5θ, for 0 < θ < 2π


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