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

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

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simplify sin(arctan(x/k))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

cos (18 0^{\circ} + x)

tan (\frac{π}{4} - x)

sin (arctan (\frac{x}{3}))

sin (18 0^{\circ} + x)

sin (tan (- 1 (x)))

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