Pre calculus

Question

I need help!

 

1)Graph the parametric curve.

x(t)=3t

y(t)+9t^2

t=1

 

2) graph the polar equation r=theta^2

 

3) graph the polar equation. r=5cos(theta)

 

4)graph. x(9)=(√t) y(t)=t+4

 

5)x(t)=t^4 y(t)=t^2

I know that the graph is in the first quadrant and swoops up and over, but I do not know if the graph starts at the orgin, or if the graph ends at the orgin

 

6)graph. (theta)=pi/4 r=2

which orgin is the point in?

 

7)[4(cos(30)+i sin(30))]^7

 

Answer 1

1)Graph the parametric curve.
x(t)=3t
y(t)+9t^2
t=1  <---why is this here?

 

If t can be any Real number, then you should observe that y = [3t]² = 9t²; this shows that the ordinary Cartesian coordinate version of this function is y = x² ...a well known parabola with vertex at the Origin.

 

2) graph the polar equation r=theta^2 ... make a table of values of theta (in radians):

theta 0  0.5   1 1.5 ...

r       0  0.25 1 2.25 ...   Graphing this (and other points will be a spiral; for each increase of angle, the radius is larger than any prior r value.

 

3) graph the polar equation. r=5cos(theta) is a circle; in rectangular coordinates, it's a circle passing through the origin and through (5,0) (in fact those are endpoints of its diameter).

 

4)graph. x(9)=(√t) y(t)=t+4 ⇐I think you have a typographical error here!

 

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7)[4(cos(30)+i sin(30))]^7  Use DeMoivre's Theorem to get answer 4⁷(cos 210 + i sin 210) ...you can clean it up knowing the sines & cosines of 210^o.