Inverse Trigonometric Identities Practice Problems Online

Given that $\cos ( \arcsin \frac {12}{13} - \arctan \frac {16}{12} ) = \frac {a }{b}$ where $a$ and $b$ are positive coprime integers, what is the value of $a+b$ ?

Let $x = \sin\left(\sin^{-1} \left(\frac{3}{5}\right) + \tan^{-1} (2)\right)$ . $x$ can be written in the form $\frac{a\sqrt{b}}{c}$ , where $a, b$ and $c$ are positive integers, $a$ and $c$ are coprime and $b$ is not divisible by the square of any prime. What is the value of $a+b+c$ ?

Details and assumptions

$\sin^{-1}$ and $\tan^{-1}$ represent the inverse of the $\sin$ and $\tan$ function, and not the reciprocal.

Which of the following is equal to

$\arccos ( - x) ?$

If $x \in (0, \pi )$ , which of the following is equal to

$\arctan ( \cot x) ?$

$\cos^{-1} \frac{a}{b} = 2 \tan^{-1} \frac{ \sqrt{72}} {12 },$ where $a$ and $b$ are positive, coprime integers. What is $a+b$ ?

Concept Quizzes

Challenge Quizzes

Inverse Trigonometric Identities

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.