Adaptive Practice
Inverse Trigonometric Functions
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Question 1 of 10
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Easy
If \( \sin^{-1} x = \frac{\pi}{6} \), what is the value of \( x \)?
Easy
Find the value of \( \cos^{-1} \left( \frac{1}{2} \right) \).
Medium
Evaluate \( \tan \left( \sin^{-1} \frac{3}{5} \right) \).
Medium
If \( y = \cos^{-1} x \), find \( \frac{dy}{dx} \).
Easy
Simplify \( \sin^{-1} x + \cos^{-1} x \) for \( x \in [-1,1] \).
Hard
Find the principal value of \( \tan^{-1} 1 + \tan^{-1} 2 \).
Hard
If \( \sin^{-1} x = \theta \), express \( \cos^{-1} \sqrt{1 - x^2} \) in terms of \( \theta \).
Medium
Evaluate \( \sin^{-1} \frac{12}{13} + \sin^{-1} \frac{5}{13} \).
Medium
Find the value of \( \tan^{-1} \left( \frac{1}{2} \right) + \tan^{-1} \left( \frac{1}{3} \right) \).
Medium
If \( \theta = \tan^{-1} x \), express \( \sin 2\theta \) in terms of \( x \).