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WZ

# Show that the curve with parametric equations $x = \sin t$, $y = \cos t$, $z = \sin^2 t$ is the curve of intersection of the surfaces $z = x^2$ and $x^2 + y^2 = 1$. Use this fact to help sketch the curve.

## $z=x^{2}$

Vector Functions

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##### Lily A.

Johns Hopkins University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

The problem is showed that the cliff with parametric equations actually called society. Why is he could talk society thing easy For two scientists Choir Issa Curve of intersection out Services The two X Square on DH X Square plus y square is equal to what Use this fact to help us catch the curve. First, the relation between ax one see have this. Actually, society seriously could decide his choir. So we have the It's the control x koi and exclaim Us last coin. It's called to sign his squire. Us signed this koi. So this is what So we have to curve is the curve of intersection of the services they go to x squared and X squared plus y squared. You got what now? That sketch to curve First way jaw to silence your squire past y square is they could want. Then choose some points on the curve. So zero one zero Theo Next to want Cyril on DH Blind zero one Next, two one zero. What? It's a point once there once. This point. No, You know Nick. Two one zero. It's a point on DH one zero one is this pond? Why, Nick to one cereal? Here It's a graph. Is this back? This is a graph of the truth

WZ

#### Topics

Vector Functions

##### Lily A.

Johns Hopkins University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp