What is the general solution for solvefor x,arctan(y/x)=0 ?

The general solution for solvefor x,arctan(y/x)=0 is No Solution for x\in\mathbb{R}

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solvefor x,arctan(y/x)=0

solve for

x, arctan (\frac{y}{x}) = 0

No Solution for x \in R

Solution steps

arctan (\frac{y}{x}) = 0

Apply trig inverse properties

arctan (\frac{y}{x}) = 0

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

\frac{y}{x} = tan (0)

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

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}

= 0

= 0

\frac{y}{x} = 0

\frac{y}{x} = 0

Solve

\frac{y}{x} = 0 :

No Solution for

x \in R

\frac{y}{x} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

y = 0

Verify Solutions

Find undefined (singularity) points:

x = 0

Take the denominator(s) of

\frac{y}{x}

and compare to zero

x = 0

The following points are undefined

x = 0

Since the equation is undefined for:

0

No Solution for x \in R

No Solution for x \in R

cos (x) = - 1, 0 \leq x < 2 π

2 cos^{2} (x) - 3 sin (x) - 2 = 0

4 sin (x) cos^{2} (x) = cos (x)

cos (x) = 3 sin (x)

tan (23 θ) + cot (23 θ) = \frac{4}{3}

What is the general solution for solvefor x,arctan(y/x)=0 ?
The general solution for solvefor x,arctan(y/x)=0 is No Solution for x\in\mathbb{R}