arctan(x/y)>0

Solution

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

No Solution for x \in R

Solution steps

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

arctan (x) > a

then

x > tan (a)

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

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 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

\frac{x}{y} > 0

Combine the intervals

and False for all x \in R

Merge Overlapping Intervals

and False for all x \in R

The intersection of two intervals is the set of numbers which are in both intervals

and

False for all

x \in R

False for all x \in R

No Solution for x \in R

cos^{2} (x) - sin^{2} (x) > 0

cos^{2} (x) > sin^{2} (x)

sec (2 x) < 0

\frac{3}{2} \cdot cos (2 x) \geq 0

sin^{2} (x) + \frac{1}{2} sin (x) > 0