Question

Graph the polar equation.P = 16 cos20帶이

Answer 1

To make the graph we need to make a table with different pairs of angles and radius.

We can start with θ = 0, and calculate the radius for different values of θ. (π/6, π/3, π/4 and so on. Then, you can join the points.

The equation for radius will be:

`\begin{gathered} r^2=16\cos 2\theta \\ r=\sqrt[]{16\cos2\theta} \\ r=4\cdot\sqrt[]{\cos2\theta} \end{gathered}`
`\begin{gathered} \text{for }\theta=0 \\ r=4\cdot\sqrt[]{\cos2\cdot0} \\ r=4\cdot\sqrt[]{\cos0} \\ r=4\cdot\sqrt[]{1} \\ r=4 \end{gathered}`

Then, in the line of θ = 0, you draw a point in the fourth circle.

Then, we get the following table of values:

θ r

04.00

π/63.72

π/43.36

π/32.83

π/20.00

Note that we can't evaluate angles whose cosine is negative (angles in quadrants 2 and 3) since we would be trying to calculate the square root of a negative number, which does not exist among real numbers. Then, we will evaluate angles in the first quadrant (already done) and the 4th quadrant.

θ r

-π/63.72

-π/43.36

-π/32.83

-π/20.00

In the last table we use negative angles, they can be "translated" to positive:

-π/6= π/6

-π/4= 7π/4

-π/3= 5π/3

-π/2= 3π/2

Now, we can draw the points:

Joining the points: