How do you simplify the expression $sin (arctan (\frac{3}{4}))$ $sin(arctan(3/4))$ ?

Question

2219 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-12T11:42:36

Using the formula $sin (arctan (x)) = \frac{x}{\sqrt{1 + x^{2}}}$ $sin(arctan(x))=x/sqrt(1+x^2)$ .

We have the equation

$sin (arctan (x)) = \frac{x}{\sqrt{1 + x^{2}}}$ $sin(arctan(x))=x/sqrt(1+x^2)$

that for your case is

$sin (arctan (\frac{3}{4})) = \frac{\frac{3}{4}}{\sqrt{1 + \frac{3}{4}}}$ $sin(arctan(3/4))=(3/4)/sqrt(1+3/4)$

$= \frac{3}{4 \sqrt{\frac{7}{4}}}$ $=3/(4sqrt(7/4))$

$= \frac{3}{2 \sqrt{7}}$ $=3/(2sqrt(7))$ .

How do you simplify the expression sin(arctan(34))sin(arctan(3/4))?