What is sin(arctan(z/y)) ?

The solution to sin(arctan(z/y)) is (zsqrt(y^2+z^2))/(y^2+z^2)

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simplify sin(arctan(z/y))

simplify

sin (arctan (\frac{z}{y}))

\frac{z y ^{2} + z ^{2}}{y ^{2} + z ^{2}}

Solution steps

sin (arctan (\frac{z}{y}))

Use the following identity:

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

= \frac{( \frac{z}{y} ) 1 + ( \frac{z}{y} ) ^{2}}{1 + ( \frac{z}{y} ) ^{2}}

Simplify

= \frac{z y ^{2} + z ^{2}}{y ^{2} + z ^{2}}

cos^{2} (4 x + \frac{π}{3})

a r sin (- 1)

\frac{1}{sin ( 40 d e g )}

\frac{ln ( x ^{2} )}{sin ( 3 x )}

a rco sin (- \frac{1}{4})

What is sin(arctan(z/y)) ?
The solution to sin(arctan(z/y)) is (zsqrt(y^2+z^2))/(y^2+z^2)