What is sin(arctan(x/4)) ?

The solution to sin(arctan(x/4)) is (xsqrt(16+x^2))/(16+x^2)

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simplify sin(arctan(x/4))

simplify

sin (arctan (\frac{x}{4}))

\frac{x 16 + x ^{2}}{16 + x ^{2}}

Solution steps

sin (arctan (\frac{x}{4}))

Use the following identity:

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

= \frac{( \frac{x}{4} ) 1 + ( \frac{x}{4} ) ^{2}}{1 + ( \frac{x}{4} ) ^{2}}

Simplify

= \frac{x 16 + x ^{2}}{16 + x ^{2}}

cos (x + 9 0^{\circ})

cos (x - \frac{π}{4})

cos (π + nπ)

cos (arcsin (3 x))

cot (9 0^{\circ} - x)

What is sin(arctan(x/4)) ?
The solution to sin(arctan(x/4)) is (xsqrt(16+x^2))/(16+x^2)