Does the curve defined by the polar equation
r=sec(theta)+tan(theta) intersect the vertical line x=2? How do I come about this question?.. Does the curve defined by the polar equation
r=sec(theta)+tan(theta) intersect the vertical line x=2? How do I come about this question?.. @Mathematics

Question

Does the curve defined by the polar equation
r=sec(theta)+tan(theta) intersect the vertical line x=2? How do I come about this question?..  Does the curve defined by the polar equation
r=sec(theta)+tan(theta) intersect the vertical line x=2? How do I come about this question?..  @Mathematics

jamesj · Answer

In polar coordinates
x = r cos(theta)
y = r sin(theta)

Hence you write down an equation for x as a function of theta.

Then see if that expression is ever equal to 2.

jamesj · Answer

$$ x(\theta) = r \cos(\theta) = ... $$

anonymous · Answer

so then $$x= (\sec \theta + \tan \theta)\cos \theta?$$

jamesj · Answer

Now simplify that expression.

anonymous · Answer

$$x = 1 + \sin \theta$$
so then I just insert 2?

jamesj · Answer

The question is is there a theta such that x = 2 i.e.,
1 + sin(theta) = 2?

jamesj · Answer

and once you've found an answer, or the answers, and that answer isn't "there are no such theta", double check to make sure that the values of theta are in the domain of r(theta) as originally given.

anonymous · Answer

ahhh thank you!!

jamesj · Answer

You should sketch the graph of r for theta 0 to pi/2 to see what's going on.