When does the small angle approximation deviate by more than 1%?

[Airsteve0]

Homework Statement

Find, by comparison with exact trigonometry, the angle,  (provide a numerical value
in degrees), above which the small angle approximation departs from the exact result by more than 1 percent.

Homework Equations

Approx.: d = s = rθ
Exact: d = 2*r*Sin(θ/2)

The Attempt at a Solution

.01 = |Exact - Approx.|/Exact

(θ/2)*Csc(θ/2) = 1.01


At this point I am unsure of how to isolate for θ. Any tips are greatly appreciated, thanks!

 

[SammyS]

Homework Statement

Find, by comparison with exact trigonometry, the angle,  (provide a numerical value
in degrees), above which the small angle approximation departs from the exact result by more than 1 percent.

Homework Equations

Approx.: d = s = rθ
Exact: d = 2*r*Sin(θ/2)

The Attempt at a Solution

.01 = |Exact - Approx.|/Exact

(θ/2)*Csc(θ/2) = 1.01

At this point I am unsure of how to isolate for θ. Any tips are greatly appreciated, thanks!

That equation can only be solved numerically or graphically.

Don't forget to change the angle to degree measure.