What is the general solution for solvefor x,arctan(y/x)= pi/4 ?

The general solution for solvefor x,arctan(y/x)= pi/4 is x=y

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solvefor x,arctan(y/x)= pi/4

solve for

x, arctan (\frac{y}{x}) = \frac{π}{4}

x = y

Solution steps

arctan (\frac{y}{x}) = \frac{π}{4}

Apply trig inverse properties

arctan (\frac{y}{x}) = \frac{π}{4}

arctan (x) = a \Rightarrow x = tan (a)

\frac{y}{x} = tan (\frac{π}{4})

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

\frac{y}{x} = 1

\frac{y}{x} = 1

Solve

\frac{y}{x} = 1 : x = y

\frac{y}{x} = 1

Multiply both sides by

x

\frac{y}{x} = 1

Multiply both sides by

x

\frac{y}{x} x = 1 \cdot x

Simplify

y = x

y = x

Switch sides

x = y

x = y

(1 + cos (x)) (tan (x) - 1) = 0

cos (x) = \pm \frac{1}{2}

\frac{cos ( θ )}{1 + sin ( θ )} = tan (\frac{π}{4} - θ)

sin (x) = \frac{1}{4 sin ( x )}

cos (4 θ) = cos (3 θ)

What is the general solution for solvefor x,arctan(y/x)= pi/4 ?
The general solution for solvefor x,arctan(y/x)= pi/4 is x=y