Trigonometry: Deriving the Sine Function
description
Transcript of Trigonometry: Deriving the Sine Function
Trigonometry:Deriving the Sine FunctionSuganya Chandrakumar & Humaira Masehoor
Connection to the Curriculum
CourseMCF3M: Functions and Applications
StrandTrigonometry
Expectation2.4 Sketch the graph of f(x) = sinx for angle measures expressed in degrees, and determine and describe its key properties (i.e., cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/decreasing intervals)
Learning Goals
Students will:1. Develop a clear
understanding of the unit circle
2. Make a connection between the unit circle and the sine function
Agenda for the Day
Ferris Wheel VideoReview on the Unit Circle
Spaghetti TrigTicket out the Door
Ferris Wheel
While watching the video, I want you think about…
When you ride on a Ferris wheel does your motion have anything in common with a wave?
Unit Circle Review• When you work with angles in all four
quadrants, the trig ratio for those angles are computed in terms of the values x, y, & r
• Where r is the radius of the circle that corresponds to the hypothesis of the right angle triangle for your angle
• The x and y values on the unit circle are defined as:
x = cos(ϴ)y = sin(ϴ)r = 1P = (x,y) = (cos(ϴ), sin(ϴ))
Sine Function• Looking at the sin ratio in the four quadrants, we can take the input (the
angle measure ϴ), “unwind” this to form the unit circle and put it on the horizontal axis of a standard graph in the x,y-plane.
• Then we can take the output (value of sin(ϴ)) and use this value as the height of the function.
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