Given that

, then

The slope of a tangent line in the polar coordinate is given by:

Thus, we have:

Part A:
For horizontal tangent lines, m = 0.
Thus, we have:

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,

Thus, we have:

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
Answer: 72° or any muliple of it: 72°, 144°, 216°, 288°, 360°, ...
It can be either clockwise or counterclockwise.
Explanation:
Thi is because a regular pentagon has 5 congruent sides.
Then you determine the angle of rotation by dividing 360° (a complete turn) by the number of sides (5)
360° / 5 = 72°.
Then every 72° the segments of the image will overlap those of the preimage.
To find the percent of 608 of 835 million, we do:
608 ÷ 845, 000, 000 = 0.0000007.19