PreCalculus

Doug Ray, Oct 1, 2016

Apps and Demonstrations for teaching / learning PreCalculus

Table of Contents

  1. Chapter 6 -- Intro to Trig Functions
    1. Unit Circle Points
    2. Creating the Sine Graph
    3. Sally's Path
  2. Chapter 7 -- Trigonometry
    1. Is y = sin(x) one-to-one?
    2. Is y = cos(x) one-to-one?
    3. Rectangle Inscribed in Semicircle

1.

Chapter 6 -- Intro to Trig Functions

Chapter 6 -- Introduction to Trigonometric Functions

  • 1. Unit Circle Points
  • 2. Creating the Sine Graph
  • 3. Sally's Path

1.1.

Unit Circle Points

Points on the Unit Circle
As the standard position angle [math]\theta[/math] changes, the point [math]P[/math] on the terminal side of the angle and on the unit circle also moves around. The coordinates for point [math]P[/math] are shown at the top.[br][br]Note that [math]\cos\theta=x[/math] and [math]\sin\theta=y[/math] from the coordinates of the point [math]P\left(x,y\right)[/math].[br][br]The special angles of [math]30^{\circ}[/math], [math]45^{\circ}[/math], and [math]60^{\circ}[/math] reveal the exact fractional form of those angles.
What is the value of [math]\cos26^{\circ}[/math]?
– Doug Ray

1.2.

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1.3.

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2.

Chapter 7 -- Trigonometry

  • 1. Is y = sin(x) one-to-one?
  • 2. Is y = cos(x) one-to-one?
  • 3. Rectangle Inscribed in Semicircle

2.1.

Is y = sin(x) one-to-one?

One-to-one
Is [math]y=\sin x[/math] a one-to-one function?
Move the left slider to a point on the left and the right slider to a point on the right where the highlighted portion of the graph is one-to-one.[br][br]What restriction should be used so that [math]y=\sin x[/math] is one-to-one and the full range of the function is used?
– Doug Ray

2.2.

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2.3.

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