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

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

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simplify cos(arctan(x/y))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

sin (x + \frac{7 π}{6})

cos (x + x)

cos (x) + cos (- x)

tan (- θ)

sin (arccos (3 x))

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