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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