The Inverse Trigonometric Functions

Lecture 1: The Inverse Trigonometric Functions

Lecture 2: Filling out Unit Circle

Examples

1. Find the exact value of each expression in radians. If there is no value, write undefined.   SOLUTION

  (a)  \( \tan^{-1} 1\)    (b)  \(\sin^{-1} 2\)    (c)  \(\tan^{-1} \left(- \sqrt{3}\right)\)    (d)  \(\cos^{-1} \left(-\dfrac{\sqrt{3}}{2}\right)\)    (e)  \(\sin^{-1} \left( \sin \dfrac{3\pi}{4} \right)\)    (f)  \(\tan^{-1} \left( \tan \dfrac{\pi}{4} \right)\)

2. Find the exact value of each expression in radians. If there is no value, write undefined.   SOLUTION

(a)  \(\cos^{-1} (-2)\)    (b)  \(\sin^{-1} 1\)    (c)  \(\tan^{-1} \left(-1\right)\)    (d)  \(\sin^{-1} \left(\dfrac{\sqrt{3}}{2}\right)\)    (e)  \(\cos^{-1} \left( \cos \dfrac{3\pi}{4} \right)\)    (f)  \( \tan^{-1} \left( \tan \dfrac{3\pi}{4} \right)\)  

3. Find the exact value of each expression in radians. If there is no value, write undefined.  SOLUTION

(a) \(\cos^{-1} \left(\cos\dfrac{4\pi}{5} \right)\)   (b) \( \tan^{-1} \left(\tan\dfrac{4\pi}{5} \right)\)  (c)  \(\sin^{-1} \left(\sin\dfrac{5\pi}{4}\right)\) (d) \( \tan^{-1} \left(\tan\dfrac{5\pi}{6} \right)\)  (e)   \(\cos^{-1} \left( \cos \dfrac{8\pi}{7} \right)\)