Thread: parameterized curves that lie in R3

which image of the given parameterized curves lie on the unit sphere in R3?

1. r(x)=(sin(3x), 0, cos(3x))
2. r(x)=(x^2, cos x, sin x)
3. r(x)=(1/sqrt.2, (-cos x)/sqrt.2, (sin x)/sqrt.2)
4. r(x)= (sec x, 1/sqrt.2, cos x)

How do you actually go about determining this?

For a given parametrized curve the image lie on the unit sphere of iff for all . For example satisfies it because for all .


Fernando Revilla