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Inverse Trigonometric Functions: Problems with Solutions
A list of problems on inverse trigonometric functions.
Problem 1
Calculate: [tex]sin(2arccos\frac{3}{5}) = ?[/tex]
Solution:
Let's arc cos 3/5 = x;
then cos x = 3/5; 0 < x < π/2
So [tex]sin2x=2sin x cos x = 2\sqrt{1-\frac{9}{25}}.\frac{3}{5} = \frac{24}{25}[/tex]
Problem 2
Calculate: [tex]sin(arcsin\frac{3}{5} + arcsin\frac{8}{17})[/tex]
Solution:
No solution is available. The answer is 77/85.
Problem 3
[tex]tan(arcsin\frac{12}{13}) = ?[/tex]
Solution:
Answer: 12/5
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