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GDC Set up Ensure that your calculator is in degree mode and that you know how to adjust the v-window of your graphs before doing these trigonometry graphs.

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**Amplitude of sine graphs**

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**Amplitude of cosine graphs**

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**Amplitude of a trig graph**

A graph of y=sin(x) is shown below. This graph has an amplitude of 1. The graph of y=2sin(x) has an amplitude of 2. The graph of y=3sin(x) has an amplitude of 3. This pattern will also work with cosine graphs.

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**Amplitude of trig. graphs**

You will have discovered from previous slides that multiplying a trig graph by a number stretches the graph. The multiplying factor of the graph is known as the graph’s amplitude.

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**Amplitude of trig graphs 1**

Find the amplitude of the graph below.

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**Amplitude of trig graphs 2**

Find the value of a in f(x)=asinx, graphed below.

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Period of sine graphs

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**Period of cosine graphs**

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**Period of a trig graph A graph of y=cos(x) is shown below.**

This graph has an period of 360 - the length it takes to make a complete wave. The graph of y=cos(2x) has an period of 180. The graph of y=cos(3x) has an period of 120.

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Period of trig. graphs You will have discovered from previous slides that multiplying the x by a constant increases the number of ‘waves’ the graph does. This is called the period - the time it takes to complete one cycle.

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Period of trig. graphs Find the period of each of these graphs.

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Period of trig graphs 1 Find the period of the graph below.

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**Vertical shift of trig. graphs**

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**Vertical shift of trig. graphs**

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**Shift of a trig graph A graph of y=cos(x) is shown below.**

Look at where this graph starts (0,1). The graph of y=cos(x)+2 has a shift of 2. The graph of y=cos(x)-3 has a shift of -3 This pattern will also work with sine graphs.

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**Vertical shift of trig. graphs**

You will have discovered from previous slides that adding a constant onto the trig graph will move the graph up, or down if the constant is negative. Write down the y-coordinate where the graph crosses the y-axis for each of these functions.

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**Putting it all together**

Amplitude Vertical shift Calculates the period This is the general expression for a trig. graph which has been transformed. If you are trying to find the values of the letters then find a first, b second and c last. This format also works for cosine and tangent graphs.

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Finding a, b and c

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Finding a, b and c

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Finding a, b and c

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Finding a, b and c

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