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

The solution to sin(arctan(L/z)) is (Lsqrt(z^2+L^2))/(z^2+L^2)

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simplify sin(arctan(L/z))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

θ cos (- 77 0^{\circ})

sin (2 π - a)

sin (\frac{2 π t}{3} + 8 π)

sin (9 0^{\circ} - x) (sec (x))

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

What is sin(arctan(L/z)) ?
The solution to sin(arctan(L/z)) is (Lsqrt(z^2+L^2))/(z^2+L^2)