Introduction to polar coordinates

The student will be introduced to the definition of polar coordinates, how to graph them, and how to compare them to rectangular coordinates.

A lesson plan for grades 9–12 Mathematics

By vicky burlington

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Related topics

• Learn more about algebra, coordinate plane, graphing, mathematics, polar coordinates, and polar equations.

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Learning outcomes

Students will:

• know the basic reference for polar coordinates.
• learn how to locate a point in polar coordinates.
• compare a point given in polar coordinates to a point given in rectangular coordinates.

Teacher planning

Time required for lesson

50 minutes

Materials/resources

• graph paper
• overhead transparencies of coordinate plane and polar coordinate plane

Technology resources

• scientific calculator
• overhead projector

Pre-activities

Review the 30-60-90 and 45-45-90 triangle relationships by doing some examples.

Activities

1. The teacher will put up a prepared transparency with problems to find the missing sides of several 30-60-90 and 45-45-90 right triangles. Students will work on these for about 5 minutes and then answers will be checked and the problems discussed.
2. The teacher will discuss how the points in a plane can be located. In math, we usually use a pair of coordinate axes and locate points in relation to their points of intersection, the origin. Ask: “Could there be other ways of locating points?” Let students discuss and make suggestions. Carefully consider each suggestion. Don’t discourage creativity! Have students look at the pros and cons of each suggestion.
3. Offer students the possibility of locating points in a plane by choosing a point (called the origin), a ray with its endpoint at the origin, and a direction of rotation. A point could be located by giving its distance from the origin and the angle of rotation.
4. Use two transparencies, one with the rectangular coordinate plane and the other with a polar coordinate plane. The units on the x-axes must be congruent. Graph the point (2,2) on the rectangular coordinate plane. Overlay the polar plane and ask students how they could locate the point by giving a radius and angular rotation of the ray. (They should notice the 45-45-90 triangle relationship and be able to calculate the radius.)
5. Give students a list of points in polar or rectangular coordinates and have them convert to the other form. Use points that fit the 30-60-90 or 45-45-90 form.
6. (Optional) Challenge more advanced students to derive formulas for changing from polar to rectangular and vice-versa.

Assessment

Immediate assessment:
Walk around the room and check student answers as they work on these problems.

Give a quiz the next day to see if they understood the concept of changing from rectangular to polar and vice-versa.