Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- xy>-4
- (log(x^2+9)/log(3))*log((4/5))*(3*x)/(x+2)-log((4/5))*(6-x)<=0
- (2^2-x)>2c-3
- 1-x>3-2*x
- Derivative of:
-
tan(x+pi/4)
-
Identical expressions
- tan(x+pi/ four)< one
- tangent of (x plus Pi divide by 4) less than 1
- tangent of (x plus Pi divide by four) less than one
- tanx+pi/4<1
- tan(x+pi divide by 4)<1
-
Similar expressions
- tan(x-pi/4)<1
- |tan(x+pi/(4))|>=1
tan(x+pi/4)<1 inequation
The solution
You have entered
[src]
/ pi\ tan|x + --| < 1 \ 4 /
$$\tan{\left(x + \frac{\pi}{4} \right)} < 1$$
tan(x + pi/4) < 1
Detail solution
Given the inequality:
$$\tan{\left(x + \frac{\pi}{4} \right)} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x + \frac{\pi}{4} \right)} = 1$$
Solve:
Given the equation
$$\tan{\left(x + \frac{\pi}{4} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{4} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n$$
$$x_{1} = \pi n$$
$$x_{1} = \pi n$$
This roots
$$x_{1} = \pi n$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\pi n + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x + \frac{\pi}{4} \right)} < 1$$
$$\tan{\left(\left(\pi n - \frac{1}{10}\right) + \frac{\pi}{4} \right)} < 1$$
the solution of our inequality is:
$$x < \pi n$$
$$\tan{\left(x + \frac{\pi}{4} \right)} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x + \frac{\pi}{4} \right)} = 1$$
Solve:
Given the equation
$$\tan{\left(x + \frac{\pi}{4} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{4} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n$$
$$x_{1} = \pi n$$
$$x_{1} = \pi n$$
This roots
$$x_{1} = \pi n$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\pi n + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x + \frac{\pi}{4} \right)} < 1$$
$$\tan{\left(\left(\pi n - \frac{1}{10}\right) + \frac{\pi}{4} \right)} < 1$$
/ 1 pi \ tan|- -- + -- + pi*n| < 1 \ 10 4 /
the solution of our inequality is:
$$x < \pi n$$
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Solving inequality on a graph
Rapid solution 2
[src]
pi (--, pi) 4
$$x\ in\ \left(\frac{\pi}{4}, \pi\right)$$
x in Interval.open(pi/4, pi)
Rapid solution
[src]
/pi \ And|-- < x, x < pi| \4 /
$$\frac{\pi}{4} < x \wedge x < \pi$$
(x < pi)∧(pi/4 < x)