# What is the slope of the tangent line of r=theta-sin((theta)/6+(2pi)/3) at theta=(pi)/6?

Aug 14, 2018

Slope of tangent line at $\theta = \frac{\pi}{6}$ is $1.096$

#### Explanation:

r=theta-sin(theta/6+(2 pi)/3); theta= pi/6

(dr)/(d theta)= 1 -cos (theta/6+(2 pi)/3)*1/6;

Slope of tangent line at $\theta = \frac{\pi}{6}$ is

(dr)/(d theta)(pi/6)= 1 -cos (pi/36+(2 pi)/3)*1/6;  or

$\frac{\mathrm{dr}}{d \theta} \left(\frac{\pi}{6}\right) \approx 1.096 \left(3 \mathrm{dp}\right)$

Slope of tangent line at $\theta = \frac{\pi}{6}$ is $1.096$ [Ans]