Inverse Trigonometric Functions: Problems with Solutions

A list of problems on inverse trigonometric functions.
Problem 1
Determine the measure of $\angle I$.

Problem 2
Calculate $m\angle E=$

Problem 3
Determine the measure of $\angle B$.

Problem 4
Determine the measure of $\angle A$.

Problem 5
$\frac{\arccos (1-8\cos ^{2}x+8\cos ^{4}x)}{x}=4\qquad x \in (0,\pi]$
Problem 6
$\arcsin \frac{\pi }{2}+\arccos \frac{\pi }{2}=\frac{\pi }{2}$
Problem 7
If $\arccos \left( a\right) < \arccos \left( b \right) \Longrightarrow a < b$
Problem 8
If $0\leq P\leq \pi $, find the value of $P=\arcsin (\frac{\sqrt{2}}{2})+\arccos (-\frac{1}{2})+\arctan(1)$
Problem 9
$\cos \left( \arctan \frac{\sqrt{6}}{2}-\arccos \frac{1}{5}\right)= $
Problem 10
Calculate: [tex]\sin(2arccos\frac{3}{5}) = ?[/tex]

Problem 11
Calculate: [tex]sin(arcsin\frac{3}{5} + arcsin\frac{8}{17})[/tex]
Problem 12
[tex]tan(arcsin\frac{12}{13}) = ?[/tex]
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