Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x=18-x
-
Equation 9*x^2=54*x
-
Equation cos(x)=-2
-
Equation 2*x^2+6*x+9=
- Express {x} in terms of y where:
- 14*x+16*y=-3
- -10*x-18*y=15
- 20*x+5*y=-3
- 4*x+18*y=-14
- Integral of d{x}:
- 1/sin(x)
- Graphing y =:
- 1/sin(x)
- Derivative of:
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1/sin(x)
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Identical expressions
- one /sin(x)
- 1 divide by sinus of (x)
- one divide by sinus of (x)
- 1/sinx
- 1 divide by sin(x)
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Similar expressions
- (cos(x)+1)/sin(x)=0
- 1/sinx
- 1/sinx
1/sin(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{1}{\sin{\left(x \right)}} = 0$$
transform
$$\frac{1}{\sin{\left(x \right)}} = 0$$
$$\frac{1}{\sin{\left(x \right)}} = 0$$
Do replacement
$$w = \sin{\left(x \right)}$$
Given the equation:
$$\frac{1}{w} = 0$$
Multiply the equation sides by the denominator w
we get:
Move free summands (without w)
from left part to right part, we given:
$$0 = -1$$
This equation has no roots
do backward replacement
$$\sin{\left(x \right)} = w$$
Given the equation
$$\sin{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
substitute w:
$$\frac{1}{\sin{\left(x \right)}} = 0$$
transform
$$\frac{1}{\sin{\left(x \right)}} = 0$$
$$\frac{1}{\sin{\left(x \right)}} = 0$$
Do replacement
$$w = \sin{\left(x \right)}$$
Given the equation:
$$\frac{1}{w} = 0$$
Multiply the equation sides by the denominator w
we get:
False
Move free summands (without w)
from left part to right part, we given:
$$0 = -1$$
This equation has no roots
do backward replacement
$$\sin{\left(x \right)} = w$$
Given the equation
$$\sin{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
substitute w: