Lecture 5 - Parametric equations
When the cycloid is first introduced, the position of a point, P, on the circumference is described as (all the following are vectors)
OP = OA + BA + BP
BP = < -asinTheta, -acosTheta >
I don't understand this as I thought
x = rcosTheta
y = rsinTheta
Therefore should the components of BP be,
BP = < -acosTheta, -asinTheta >?
OCW Scholar - Multivariable Calculus
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
yes, for a circle centered at the origin, and measuring theta counter-clockwise from the x-axis, then the points on it circumference have coords
\[ x= r \cos \theta \ , y= r \sin \theta \]
but in this problem, the angle is measured in a "non-standard" way.
Thanks for replying so quickly.
So essentially when going clockwise sin and cos give the opposite coordinates to what they give when going anti-clockwise?
the other difference is we are measuring theta from the line pointing straight-down (i.e. parallel to the negative y-axis). this switches which "leg" is sin and cos (as compared to using the positive x-axis as the start)