This activity is intended to supplement Trigonometry, Chapter 6, Lesson 4.
Time Required: 15 minutes
Students will explore what is necessary to understand the calculus of polar equations. Students will graphically and algebraically find the slope of the tangent line at a point on a polar graph. Finding the area of a region of a polar curve will be determined using the area formula.
Topic: Polar Equations
Find the slope of a polar equation at a particular point.
Find the area of polar equation.
Teacher Preparation and Notes
Make sure each students' calculator is in RADIANS (RAD) and POLAR (POL) in the MODE menu.
Plotting Coordinates & Exploring Polar Graphs
Students begin the activity by plotting points on a polar graph. This should be a refresher of polar coordinates for most students. Students practice using the calculator to graph a polar equation.
What do you think it means to have a negative angle, like (−π3,3)?
What about if r was negative? For example, move to (π2,−6).
1. See image below.
2. If r(θ)=cos(θ),r(π3)=0.5.
3. a heart or cardioid
4. A circle is in the form r=a, where a is a constant.
A polar rose with even petals is in the form r(θ)=a⋅sin(nθ), where n is even.
A polar rose with odd petals is in the form r(θ)=a⋅sin(nθ), where n is odd.
A limaçon with an inner loop comes form r(θ)=b+a⋅cos(θ), where b<a.