Inverse trigonometry Knowledge-Based Download PDF

Questions

1. 1.

   What is the real value of $x$ that satisfies the equation $\arcsin(2x) = \arccos(x)$?

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

   What is the exact value of $\tan\left(\frac{1}{2}\arccos\left(\frac{7}{25}\right)\right)$?

   • A) $\frac{3}{4}$
   • B) $\frac{4}{3}$
   • C) $\frac{3}{5}$
   • D) $\frac{1}{2}$
3. 3.

   What is the exact value of $\cos\left(2\arctan(3)\right)$?

   • A) $\frac{4}{5}$
   • B) $-\frac{3}{5}$
   • C) $\frac{3}{5}$
   • D) $-\frac{4}{5}$
4. 4.

   What is the exact value of $\sin\left(\arccos\left(\frac{5}{13}\right) - \arctan\left(\frac{3}{4}\right)\right)$?

   • A) $\frac{16}{65}$
   • B) $\frac{27}{65}$
   • C) $\frac{63}{65}$
   • D) $\frac{33}{65}$
5. 5.

   What is the exact value of $\sin\left(2\arccos\left(-\frac{4}{5}\right)\right)$?

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