Lesson 6

1. Lesson 6

1.6. Connect

Mathematics 30-1 Module 4

Module 4: Foundations of Trigonometry

Connect

Lesson 6 Assignment

Complete the Lesson 6 Assignment that you saved in your course folder at the beginning of the lesson. Show work to support your answers.

Save your work in your course folder.

Project Connection

There is no Project Connection in this lesson.

Going Beyond

Polar Coordinates

If r is negative, the point reflects across the origin.

A point on the x-axis one third of a unit from the origin has been shown to rotate counterclockwise pi divided by 4 radians. This results in the coordinates of the terminal arm being one third, pi divided by 4. This point is then shown reflected across the origin and results in the coordinates of the terminal arm being negative one-third, pi divided by 4.

Source: Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011.
Reproduced with permission.

Another way of representing trigonometric functions is to use polar coordinates. In this system the coordinates (r, θ) represent a radius and an angle of rotation. In the first diagram, the radius of the terminal arm is and the angle is Use the table of values you created in Try This 2 to plot r = sin θ on a polar grid.

A point on the x-axis one half a unit from the origin has been shown to rotate counterclockwise pi divided by 6 radians. This results in the coordinates of the terminal arm being one half, pi divided by 6.

Use the following polar grid to create your graph of r = sin θ.

This diagram shows a polar grid with radius increments of 0.5 and angle increments of pi divided by 6.

Use Polar Functions Explorer to check your graph.