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JSGhost
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Homework Statement
Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.
r = 9sin(θ)
θ = pi/6
Homework Equations
dy/dx = (dy/dθ) / (dx/dθ)
x=rcosθ
y=rsinθ
(sinx)^2 = (1/2)(1-cos2x)
(cosx)^2 = (1/2)(1+cos2x)
2sinxcosx = sin(2x)
The Attempt at a Solution
r = 9sin(θ)
x=rcos(θ)=9sin(θ)cos(θ)= --> Would this be sin(9θ) or sin(18θ)?
y=rsin(θ)=9sin(θ)sin(θ)= 9sin^2(θ)dy/dx = (dy/dθ) / (dx/dθ) = (9 * 9sinθcosθ) / (cos(18θ) * 9) = sin(18θ)/cos(18θ) = tan(18θ)
θ = pi/6
tan(18*pi/6)=tan(3pi)=0