Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x=18-x
-
Equation x^4=(2*x-3)^2
-
Equation 9*x^2=54*x
-
Equation cos(x)+sin(x)=0
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 7*x-2*y=20
- -1*x-20*y=-17
- 9*x+18*y=3
- Integral of d{x}:
- 1/sin(x)
- Graphing y =:
- 1/sin(x)
- Derivative of:
-
1/sin(x)
-
Identical expressions
- one /sin(x)
- 1 divide by sinus of (x)
- one divide by sinus of (x)
- 1/sinx
- 1 divide by sin(x)
-
Similar expressions
- 1/sinx
- (cos(x)+1)/sin(x)=0
- 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: