Polar areas and tangents, FP2

6_1_polar_example_2

Practice with Pol( , ) and Rec( , )

ex7a

Or, in radians: 1a. 1.176, b. 1.965, c. −1.965, d. −0.983, e. −π/6

Sketching graphs in polar coordinates

Plot these, leaving out all parts where the formula gives you a negative value for r

r = cos θ

r = 1 + cos θ

r = cosec θ

r = sec θ

Without plotting, do a rough sketch of

r = cosec (θ−π/3)

r = 10 + cos θ

r = 2

θ = π/4

Ex 7c polars

More: Ex.7C Q.4-6

Polar graphs and areas

Integration formula

The infinitesimals are sectors, not tiny rectangles

Using double-angle formulas for integration

Ex.7D Q.1-9

Overlap areas

Example 10 from textbook

Area of overlap of the curves

r = 2 + cos θ

r = 5 cos θ

example10

Ex.7D Q.10 and 11

Tangents

Ex.7E.