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>
Idk if this will help, but her :)
Answer:
36 <127
(36,127°)
36 [ cos (127) + i sin (127)]
Step-by-step explanation:
w1 = 2 < 95
w2 = 18 < 32
w1 * w2
We multiply the magnitude and add the angles
w1 * w2 = 2*18 < (95+32)
=36 < 127
36 [ cos (127) + i sin (127)]
3 1/2 divided by 2 1/4 = 1.55555556
1.55555556 Rounded is 1.55
Answer:
about 7 units
Step-by-step explanation:
10