The Inverse Trigonometric Functions
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) \(\cos^{-1} \left(-\frac{1}{2} \right)\)
(b) \( \tan^{-1} 1\)
(c) \(\sin^{-1} \left(\frac{\sqrt 2}{2}\right)\)
(d) \(\sin^{-1} \left(\sqrt{3}\right)\)
(e) \(\cos^{-1} \left( \cos \dfrac{7\pi}{6} \right)\)
(f) \(\tan^{-1} \left( \tan \dfrac{5\pi}{4} \right)\)
4. Find the exact value of each expression.
SOLUTION
(a) \( \cos \left[ \sin^{-1}\left( \frac{\sqrt
2}{3}\right)\right] \) (b)
\(\tan \left[ \cos^{-1}\left( -\frac{1}{3}\right)\right]\)
5. Find the exact value of each expression.
SOLUTION
(a) \(\tan \left[ \cos^{-1}\left(
\frac{2}{3}\right)\right] \) (b)
\(\sin \left[ \tan^{-1}\left(- \frac{12}{5}\right)\right]\)
6. Find the exact value of each expression.
SOLUTION
(a) \(\sec \left[ \tan^{-1}\left(
-\frac{1}{4}\right)\right] \) (b)
\(\cos \left[ \sin^{-1}\left( \frac{15}{17}\right)\right]\)