2) For what inputs does the function cross the x-axis? Why does this happen? Be specific.
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3) For what inputs does the function reach its maximum output? Its minimum output? What is that value? How does this value relate to the circle?
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3.a) Notice that this height is measured from centerline of the graph. Look at the vertical symmetry around this centerline! In this case the centerline is the x-axis, but think of it as the centerline of the function. This height is called the AMPLITUDE.
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4) Think about where the function has positive outputs and negative outputs. How does this connect to quadrants in the circle? Think about what we talked about in the last unit.
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5) As you increase the angle, look to see if the function (outputs) are increasing or decreasing. How does this relate to the circle as the angle increases? Think about what we talked about in the last unit.
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6) Notice how the cycle of the graph repeats. How long does it take to complete ONE cycle? This is called the function's PERIOD. Think about how this period length relates to the circle!
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7) If you haven't already done so, draw a sketch of one period of f(x)= cos x staring at the origin. Make sure you scale your axes! Labeling that sketch with important information from this investigation would be a great idea!
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Don't touch this; it contains all the things that make the graph work.
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Trigonometry: Period and Amplitude
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Trigonometry: Phase
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Trigonometry: Unit Circle
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Conic Sections: Circle
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Conic Sections: Parabola and Focus
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Polar: Rose
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Polar: Limacon
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Polar: Conic Sections
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Parametric: Introduction
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Parametric: Cycloid
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Transformations: Translating a Function
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Transformations: Scaling a Function
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Transformations: Inverse of a Function
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Statistics: Linear Regression
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Statistics: Anscombe's Quartet
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Statistics: 4th Order Polynomial
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Lists: Family of sin Curves
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Calculus: Derivatives
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Calculus: Tangent Line
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Calculus: Taylor Expansion of sin(x)
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Calculus: Integrals
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Calculus: Integral with adjustable bounds
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Calculus: Fundamental Theorem of Calculus
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