Inverse trigonometry Knowledge-Based Practice

Questions

1. 1.

   What is the real solution to the equation $\arcsin(x) + \arcsin(2x) = \frac{\pi}{2}$?

   • A) $\frac{\sqrt{5}}{5}$
   • B) $\frac{\sqrt{3}}{3}$
   • C) $\frac{1}{3}$
   • D) $\frac{\sqrt{5}}{10}$
2. 2.

   What is the real solution to the equation $\arctan(2x) + \arctan(3x) = \frac{3\pi}{4}$?

   • A) $-\frac{1}{6}$
   • B) $\frac{1}{2}$
   • C) $1$
   • D) $2$
3. 3.

   What is the exact value of $\tan\left(2\arctan\left(\frac{1}{2}\right) - \arctan\left(\frac{1}{3}\right)\right)$?

   • A) $\frac{5}{13}$
   • B) $\frac{7}{11}$
   • C) $\frac{9}{13}$
   • D) $\frac{11}{17}$
4. 4.

   What is the exact value of $\cos\left(\arcsin\left(\frac{4}{5}\right) - \arctan\left(\frac{7}{24}\right)\right)$?

   • A) $\frac{44}{125}$
   • B) $\frac{3}{5}$
   • C) $\frac{4}{5}$
   • D) $\frac{117}{125}$
5. 5.

   What is the exact value of $\sin\left(2\arccos\left(-\frac{3}{5}\right)\right)$?

   • A) $\frac{24}{25}$
   • B) $-\frac{24}{25}$
   • C) $-\frac{7}{25}$
   • D) $\frac{7}{25}$

Answers and step-by-step solutions appear after you finish the test.