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Back to The Chain Rule

Exercise 3

Avg difficulty 2.5

Consider the function k(θ)=sin⁡−1(sin⁡(θ))\fe{k}{\theta}=\fe{\sin^{-1}}{\fe{\sin}{\theta}}.

Use the chain rule and an appropriate trigonometric identity to verify your answer to this exercise. Please note that cos⁡(θ)>0\fe{\cos}{\theta}\gt0 over (−π2,π2)\ointerval{-\frac{\pi}{2}}{\frac{\pi}{2}}.

Simonds, Calculus Lab Manual, §6.5 Supplement, Exercise 3

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Adapted from Calculus Lab Manual © 2012–2016 Portland Community College. Licensed under CC BY-SA 4.0. Source: Calculus Lab Manual. Imported at revision 3060f8e.