The bifolium is a curve that can be drawn using either an Algebraic equation or

Question

The bifolium is a curve that can be drawn using either an Algebraic equation or an equation involving trigonometric functions. Even though the trigonometric equation uses polar coordinates, it's much easier to solve the trigonometric equation for function values than the algebraic equation. The graph of r = 8 sin theta cos^2 theta is shown below. You'll see more on polar coordinates and graphs of in Chapter 8. The following graph is in polar coordinates. Bifolium. The equation for the bifolium shown on the left is r = 8 sin theta cos^2 theta. Use a Pythagorean identity to rewrite the equation using only the function sin theta. Then find r if theta = 30 degree, 60 degree, and 90 degree.

Explanation / Answer

identity :sin2+cos2=1

=>cos2=1-sin2

now r=8sincos2

=>r=8sin(1-sin2)

=>r=8(sin-sin3)

=30o

=>r=8(sin30o-sin330o)

=>r=8((1/2)-(1/8))

=>r=8*3/8

=>r=3

=60o

=>r=8(sin60o-sin360o)

=>r=8((3/2)-(33/8))

=>r=3

=90o

=>r=8(sin90o-sin390o)

=>r=8(1-1)

=>r=0

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