Presentation on theme: "Trigonometric Functions – Lesson 3"— Presentation transcript:
1Trigonometric Functions – Lesson 3 REVIEW:Graph Sine and Cosine FunctionsWith amplitude and period changes.INVESTIGATE”VERTICAL SHIFTObjective: To graph sine and cosine functions with amplitude, period changes and vertical shift!
2What do trig functions model in real life? Sound wavesFerris WheelMusic frequenciesEKG’sJust as we can create linear, exponential and quadratic models to represent real life data, we can also use regression to determine whether or not a trig function would be a good model to represent the data!
3Graphing: What do we know – starting point Graphing: What do we know – starting point? f(x) = sin x and f(x) = cos x
4Range & Intercepts: f(x) = sin x and f(x) = cos x what is the shift between sin and cos?
5f(x) = sin x & two important ideas PeriodAmplitudeAmplitudePeriodPeriod means how many degrees in one cycle.Amplitude means the distance from the centre to the maximum or minimum, OR (max + min) ÷ 2
7How does “b” impact the graph?f(x) = sin x & f(x) = sin 2x What does it do?Period = 180º
8f(x) = sin x & f(x) = sin 3x So b changes the period = 360º ÷ b or = 120ºSo b changes the period = 360º ÷ b orIf _____ ____1 it’s hard to get out of the water! If _____ ___ 1 it’s easy to get out without getting slammed by a wave!
9How does “A” impact the graph How does “A” impact the graph?f(x) = sin x & f(x) = -1 sin x Is the y intercept the same? What changes?Amplitude = 1