Sketching a Parametrized Curve

Multivariable Calculus: Sketch the curve for the vector-valued function r(t) = (cos(t), sin(t), -cos(t)-sin(t) +1). We describe the trace of the curve as the intersection of a cylinder and a plane.

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[johnmorisi]

wow thanks so much. i have a test tomorrow and i was clueless. ive listened to my prof. teach us how to graph that over 1000x and I never understood it. with you i learned it in 15 minutes. thanks a lot, i owe at least 20 points of my grade to you.

[ChocoTaco]

very helpful. thank you! continue putting up videos please!

[MathDoctorBob]

You're welcome! I'm teaching College Algebra now, which is a nice break.

[MathDoctorBob]

@ChocoTaco39 You're welcome! Please let me know if you have any requests. - Bob

[MathDoctorBob]

Just caught this! You need to complete the square in x. x^2 - x = (x-1/2)^2 - 1/4. So the equation becomes (x-1/2)^2 + y^2 = 1/4. This is a circle of radius 1/2 centered at (1/2, 0) in the xy plane, (z anything). So r(u, v) = (1/2+1/2 cos(u), 0+1/2sin(u), v)

[seanmuzoka]

how would i go about parametrizing a cylinder 'not centered at the origin' say x^2+y^2=x