{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Engineering Calculus Notes 159

# Engineering Calculus Notes 159 - that the actual points...

This preview shows page 1. Sign up to view the full content.

2.2. PARAMETRIZED CURVES 147 Figure 2.15: The curve y 3 = x 2 Using the relation between polar and rectangular coordinates, this can be parametrized as −→ p ( θ ) = ( f ( θ ) cos θ,f ( θ ) sin θ ) . We consider a few examples. The polar equation r = sin θ describes a curve which starts at the origin when θ = 0; as θ increases, so does r until it reaches a maximum at t = π 2 (when −→ p ( π 2 ) = (0 , 1)) and then decreases, with r = 0 again at θ = π ( −→ p ( π ) = ( 1 , 0)). For π<θ< 2 π , r is negative, and by examining the geometry of this, we see
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: that the actual points −→ p ( θ ) trace out the same curve as was already traced out for 0 < θ < π . The curve is shown in Figure 2.16 . In this case, we can Figure 2.16: The curve r = sin θ recover an equation in rectangular coordinates for our curve: multiplying both sides of r = sin θ by r , we obtain r 2 = r sin θ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online