Question

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

Answer 1

Slope of tangent line at `theta=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=pi/6` is

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

`(dr)/(d theta)(pi/6)~~ 1.096 (3 dp)`

Slope of tangent line at `theta=pi/6` is `1.096` [Ans]