http://www.math.utah.edu/~palais/sine.html http://www.ies.co.jp/math/java/trig/index.html http://www.analyzemath.com/function/periodic.html http://math.usask.ca/maclean/sincosslider/sincosslider.html http://www.analyzemath.com/unitcircle/unitcircle.html http://biorhythms.perbang.dk/?aid=29&name=laura&d=18&m=2&y=1979&t=23&min=54 &z= 5&phy=1&emo=1&inte=1&custom_lang=en&js=&ctrl=&custom=1&js= http://www.sfu.ca/~jtmulhol/calculus applets/geogebra Worksheets/trigonometric graphs.html

Chapter 5: Trigonometric Functions and their Graphs Section 5.1: Graphing Sine and Cosine Functions Periodic Function: A function that repeats itself over regular intervals (cycles) of its domain. A function which repeats a pattern of y values at regular intervals. Sine and Cosine functions are periodic functions. http

Period The horizontal length of one complete cycle on a periodic graph. ( The period is the length of the smallest interval that contains exactly one copy of the repeating pattern measured along the horizontal axis) Sinusoidal curve A curve that oscillates repeatedly up and down from a centre line. (looks like a wave)

Periodic Functions The simplest example of periodic motion is the motion around a circle.

Chapter 5: Trigonometric Functions and their Graphs Section 5.1: Graphing Sine and Cosine Functions Periodic Function: A function that repeats itself over regular intervals (cycles) of its domain. A periodic function repeats a pattern of y values at regular intervals. Sine and Cosine functions are periodic functions. Period The horizontal length of one complete cycle on a periodic graph. ( The period is the length of the smallest interval that contains exactly one copy of the repeating pattern measured along the horizontal axis) Sinusoidal curve A curve that oscillates repeatedly up and down from a centre line. (looks like a wave)

For any point on unit circle P(x, y) x corresponds to cosine of angle y corresponds to sine of angle As P rotates around the circle the values of cos θ and sin θ change periodically P (x, y) (Cos θ, Sin θ)

In the unit circle, we know the radius is equal to one! Therefore, becomes, resulting in, An arc length measured along the UNIT CIRCLE equals the measure of the central angle in radians. Therefore, the x variable in the functions can also represent the arc length of the circle instead of the angle at the centre of circle Where represents the length of the arc from A(1, 0) to any point on the circle. In the function, the cos x is the x coordinate on the unit circle (horizontal coordinate) In the function, the sin x is the y coordinate on the unit circle (vertical coordinate) P (Cos x, Sin x) x A (1, 0)

Unit Circle sin and cos come from.notebook November 16, 2016

Midline: The horizontal line halfway between the maximum and minimum values of a periodic function Formula: 3 1 Amplitude: The distance from the midline to either the maximum y value or minimum y value of a periodic function. The amplitude is always expressed as a positive number Formula: Example: Amplitude: Midline: Period:.

Unit Circle sin and cos come from.notebook November 16, 2016

Unit Circle sin and cos come from.notebook November 16, 2016 trig ratio y=sinx angle or arc length 0.5 0.5 0.5 0.5

Unit Circle sin and cos come from.notebook November 16, 2016 y=cosx trig ratio 0.5 0.5 0.5 0.5