Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- (|x|)+(|x-3|)>=3
- 4x-3(5x+8)<_-7
- 4^x<=8^(sqrtx+sqrt1)
- 5x+25<=2x-2
- Integral of d{x}:
-
sint
- Derivative of:
-
sint
-
Identical expressions
- sint<√ three / two
- sinus of t less than √3 divide by 2
- sinus of t less than √ three divide by two
- sint<√3 divide by 2
-
Similar expressions
- sin<=-(√3)/2
- sin(t/2)>-√2/2
- sin(t)≥\/3/2
sint<√3/2 inequation
The solution
You have entered
[src]
___
\/ 3
sin(t) < -----
2
$$\sin{\left(t \right)} < \frac{\sqrt{3}}{2}$$
sin(t) < sqrt(3)/2
Detail solution
Given the inequality:
$$\sin{\left(t \right)} < \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n + \frac{\pi}{3}$$
$$t = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
This roots
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$t_{0} < t_{1}$$
For example, let's take the point
$$t_{0} = t_{1} - \frac{1}{10}$$
=
$$\left(2 \pi n + \frac{\pi}{3}\right) + - \frac{1}{10}$$
=
$$2 \pi n - \frac{1}{10} + \frac{\pi}{3}$$
substitute to the expression
$$\sin{\left(t \right)} < \frac{\sqrt{3}}{2}$$
$$\sin{\left(2 \pi n - \frac{1}{10} + \frac{\pi}{3} \right)} < \frac{\sqrt{3}}{2}$$
one of the solutions of our inequality is:
$$t < 2 \pi n + \frac{\pi}{3}$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$t < 2 \pi n + \frac{\pi}{3}$$
$$t > 2 \pi n + \frac{2 \pi}{3}$$
$$\sin{\left(t \right)} < \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n + \frac{\pi}{3}$$
$$t = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
This roots
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$t_{0} < t_{1}$$
For example, let's take the point
$$t_{0} = t_{1} - \frac{1}{10}$$
=
$$\left(2 \pi n + \frac{\pi}{3}\right) + - \frac{1}{10}$$
=
$$2 \pi n - \frac{1}{10} + \frac{\pi}{3}$$
substitute to the expression
$$\sin{\left(t \right)} < \frac{\sqrt{3}}{2}$$
$$\sin{\left(2 \pi n - \frac{1}{10} + \frac{\pi}{3} \right)} < \frac{\sqrt{3}}{2}$$
___
/ 1 pi \ \/ 3
sin|- -- + -- + 2*pi*n| < -----
\ 10 3 / 2
one of the solutions of our inequality is:
$$t < 2 \pi n + \frac{\pi}{3}$$
_____ _____
\ /
-------ο-------ο-------
t1 t2Other solutions will get with the changeover to the next point
etc.
The answer:
$$t < 2 \pi n + \frac{\pi}{3}$$
$$t > 2 \pi n + \frac{2 \pi}{3}$$
Solving inequality on a graph
Rapid solution 2
[src]
pi 2*pi
[0, --) U (----, 2*pi]
3 3
$$t\ in\ \left[0, \frac{\pi}{3}\right) \cup \left(\frac{2 \pi}{3}, 2 \pi\right]$$
t in Union(Interval.Ropen(0, pi/3), Interval.Lopen(2*pi/3, 2*pi))
Rapid solution
[src]
/ / pi\ / 2*pi \\ Or|And|0 <= t, t < --|, And|t <= 2*pi, ---- < t|| \ \ 3 / \ 3 //
$$\left(0 \leq t \wedge t < \frac{\pi}{3}\right) \vee \left(t \leq 2 \pi \wedge \frac{2 \pi}{3} < t\right)$$
((0 <= t)∧(t < pi/3))∨((t <= 2*pi)∧(2*pi/3 < t))