Solve sin(x)<- ( sqrt(2))/2

Evaluate

sin (x) < - \frac{2}{2}

Solve the equation

More Steps

x = {\frac{5 π}{4} + 2 kπ \frac{7 π}{4} + 2 kπ, k \in Z

Find the monotonically intervals

[\frac{π}{2} + 2 kπ, \frac{3 π}{2} + 2 kπ], k \in Z [\frac{3 π}{2} + 2 kπ, \frac{5 π}{2} + 2 kπ], k \in Z

Find the intersection

More Steps

\frac{5 π}{4} + 2 kπ < x \leq \frac{3 π}{2} + 2 kπ, k \in Z [\frac{3 π}{2} + 2 kπ, \frac{5 π}{2} + 2 kπ], k \in Z

Find the intersection

More Steps

\frac{5 π}{4} + 2 kπ < x \leq \frac{3 π}{2} + 2 kπ, k \in Z \frac{3 π}{2} + 2 kπ \leq x < \frac{7 π}{4} + 2 kπ, k \in Z

Solution

\frac{5 π}{4} + 2 kπ < x < \frac{7 π}{4} + 2 kπ, k \in Z

Alternative Form

x \in (\frac{5 π}{4} + 2 kπ, \frac{7 π}{4} + 2 kπ), k \in Z

Alternative Form

22 5^{\circ} + 36 0^{\circ} k < x < 31 5^{\circ} + 36 0^{\circ} k, k \in Z

Solve the inequality