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1 Starter 1) True or false? cos (x) = 1 + sin (x) Why? 2 2 2) Solve 1 + 4sin(x) = 3 for 0 < x < 360 Today we are learning... Sketching Trigonometric Graphs How to sketch a variety of trigonometric graphs. I will know if I have been successful if... I can complete a table of values using a calculator. I can plot the points from the table of values. I can state the period and amplitude of a curve.
2 Plotting y = sin(x) 1) Complete the table of values. Round your values to 2 decimal places. x y Plotting y = sin(x) 1) Complete the table of values. Round your values to 2 decimal places. x y
3 2) Plotting the points from the table. x y y = sin(x) ) State the amplitude and period. y = sin(x) -1 Amplitude = 1 Period = 360 o
4 Checklist I will know if I have been successful if... 1) I can complete a table of values using a calculator. 2) I can plot the points from the table of values. 3) I can state the period and amplitude of a curve. Desmos Let's check our answers using desmos... 1) y = cos(x) 2) y = tan(x) Challenge 3) y = 2sin(x) 4) y = sin(2x) 5) y = 3cos(4x) - 1
5 You are going to see 5 trigonometric graphs. For each one on your whiteboard write down the... Period = Amplitude = 1.
6 1. Period = 120 o Amplitude = 3 2.
7 2. Period = 180 o Amplitude = 3 3.
8 3. Period = 90 o Amplitude =
9 4. Period = 60 o Amplitude = 5 5.
10 5. Period = 40 o Amplitude = 2 Today we are learning... Sketching Trigonometric Graphs How to sketch a variety of trigonometric graphs. I will know if I have been successful if... I can complete a table of values using a calculator. I can plot the points from the table of values. I can state the period and amplitude of a curve.
11 Transformations of Trigonometric Graphs Today we are learning... How to transform graphs to change their amplitude and period. I will know if I have been successful if... I can state the period and amplitude of a curve. I can find a link between the equation of the curve and the amplitude and period. I can sketch a trigonometric curve without the aid of a table of values. Investigation Equation Amplitude Period y = sin(x) y = cos(x)
12 y = 3cos(3x) 1. Period = 120 o Amplitude = 3 y = 3sin(2x) 2. Period = 180 o Amplitude = 3
13 y = 0.5sin(4x) 3. Period = 90 o Amplitude = 0.5 y = 5cos(6x) 4. Period = 60 o Amplitude = 5
14 y = 2cos(9x) 5. Period = 40 o Amplitude = 2 Investigation Equation Amplitude Period y = sin(x) y = cos(x) y = 3cos(3x) y = 3sin(2x) y = 0.5sin(4x) y = 5cos(6x) 5 60 y = 2cos(9x) 2 40
15 Conclusion The graphs of y = acos(bx) and y = asin(bx)... have amplitude a and a period of 360 b o y = asin(x) always starts at the origin. Example 1 Sketch y = 2sin(x)
16 Example 2 Sketch y = 1.5cos(x) Practice Choosing a suitable scale, sketch the following trigonometric graphs without using a table of values. a) y = 3cos(x) b) y = 2sin(x) c) y = 0.5sin(x) d) y = -4cos(x) Challenge e) y = 2.25sin(2x)
17 Match the trigonometric equations with the graphs. Log onto desmos... 1) y = 3cos(x) 2) y = 3sin(2x) 3) y = 2sin(2x) Starter 1) Find the period and amplitude of the following a) y = 3cos(4x) b) y = tan(x) c) y = -5sin(9x) 2 2) Find the roots of the graph y = x + 5x - 24
18 Today we are learning... Graphing Trigonometric Functions How to sketch trig functions without drawing a table. I will know if I have been successful if... I know where the curve starts. I know the period and amplitude of the curve. I can sketch the graph. y = 2cos(3x) - Amplitude - Period - Origin?
19 y = 3sin(6x) - Amplitude - Period - Origin? Practice 1) y = 2cos(3x) 2) y = 4cos(2x) 3) y = sin(6x) 4) y = 3cos(12x) 5) y = -2sin(3x) 6) y = 4cos(6x) Check answers on desmos...
20 National 5 Exam Questions National 5 Exam Questions
21 Today we are learning... Graphing Trigonometric Functions How to sketch trig functions without drawing a table. I will know if I have been successful if... I know where the curve starts. I know the period and amplitude of the curve. I can sketch the graph.
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