Determine the Points Where the Tangent Lines are Horizontal or Vertical Using Parametric Equations

[@kristensmedbron1942]

Thank you. You explained the approach exceptionally well.

[@charlesairiohuodion7772]

I found this video very help...however I have a question. I understand the 0 to 2pi for horizontal tangent because of periodicity of cos. If my problem started off with y=sin7t will that change the periodicity or do i still add a 2pi to pi/2. Hope that question makes sense.

[@mirabal1238]

why did you have to add 2pi when you were solving for cosine but not when you were solving for sine

[@MrBluewaffles69]

why did you use the boundaries 0 to 2 pi for only the horizontal tangent lines?

[@MrBlash93]

extremely helpful video. I am just wondering how you determined the last two "t" values of (5pi/4) and (7pi/4)

[@Mathispower4u]

I'm glad I could help.
To get 5pi/2 I added 2pi to pi/2. To get 7pi/2, I added 2pi to 3pi/2
Since 2t = 5pi/2, I multiplied both sides by 1/2 to get 5pi/4
Since 2t = 7pi/2, I multiplied both sides by 1/2 to get 7pi/4

[@MrBlash93]

Mathispower4u Right, and thank you for responding. But why would you add two pi in the frist place to both t values? thank you

[@Mathispower4u]

Blas Hernandez Oh, because when we add 2pi (1 rotation) it would give us the next coterminal angle. If we don't find these coterminal angles we wouldn't find all 4 points. Remember coterminal angles have the same trig function values.

[@MrBlash93]

Mathispower4u Oh OK thank you. Thank you very much. I really appreciate your response

[@johnfredcornell3742]

Thanks. This was super helpful :)

[@thrb41]

Thanks a lot!

[@blushark8385]

get right handed