What is cos(arctan(y/x)) ?

The solution to cos(arctan(y/x)) is (xsqrt(x^2+y^2))/(x^2+y^2)

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simplify cos(arctan(y/x))

simplify

cos (arctan (\frac{y}{x}))

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

Solution steps

cos (arctan (\frac{y}{x}))

Use the following identity:

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

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

Simplify

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

cos (arcsin (\frac{x}{2}))

cos (\frac{π}{2} - θ)

sin (x + \frac{π}{3})

sin (x + 2 π)

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

What is cos(arctan(y/x)) ?
The solution to cos(arctan(y/x)) is (xsqrt(x^2+y^2))/(x^2+y^2)