Question

Find all theta from (-pi,pi) for which the tangent line of r=tan(theta/2) is horizontal.

I have gotten to

1/2sec^2(theta/2)*sin(theta)+tan(theta/2)*cos(theta)=0

How do I solve for 0?

Answer #1

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3)Find the unit tangent vector at t = 0 for the curve r (t) =
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find the equation of the tangent line when r=sqrt(sin0cos0) when
0(theta)=pi/4

Consider the polar curve r = 2 cos theta. Determine the slope of
the tangent line at theta = pi/4.

1.
Find the arclength of r=cos^(3)(theta/3)
2. Find the area outside r=3 and inside
r^2=18cos(2•theta)
3. Find the slope of the tangent line to r=2sin(4•theta) at
theta=pi/4

1. Find the slope of the tangent line to
r=2+sin3Θ at the point where
Θ=pi/4 Θ=theta
2. Find the area of the region that lies inside the
curve r=4*sinΘ and outside the curve r=2

9. Suppose that tan(alpha)=3/4 and pi<alpha<3pi/2. Find:
a)sin(2alpha), b)cos(2alpha).
10. Suppose that tan(alpha)=-3 and 3pi/2<alpha<2pi. Find:
a)sin(2alpha), b)cos(2alpha).
16. Given theta is an acute angle with cos(theta)=1/4 , find the
value of tan(theta/2)+tan(2theta). Hint: Find each (using half
angle or double angle formulas) and add them up.

Polar Functions
Algebraically test symmetries and include table of (r, theta)
for theta = 0, pi/6, pi/4, pi/3, pi/2.
16) r = 1 − 2 sin θ
18) r = cos(2θ)

given the polar curve r = 2(1+cos theta) find the Cartesian
coordinates (x,y) of the point of the curve when theta = pi/2 and
find the slope of the tangent line to this polar curve at theta =
pi/2

Find the equation of the tangent line to the curve
r = 2 sin θ + cos θ
at the point
( x 0 , y 0 ) = ( − 1 , 3 )

1. Find all angles
θ,0≤θ≤2π
(Double angle
formula, To two decimal places)
a) Tan theta
= 0.3, b) cos theta = 0.1, c) sin theta = 0.1,
d) sec theta
= 3

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