Mister Exam
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How to use it?
- Equation:
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Equation 1-5x=-6x+8
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Equation 1-5*x=-6*x+8
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Equation (x-2)^2=(x-9)^2
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- -7*x-7*y=-14
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Identical expressions
- Csin(x)− two .
- C sinus of (x)−2.
- C sinus of (x)− two .
- Csinx−2.
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Similar expressions
- Csinx−2.
Csin(x)−2. equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$c \sin{\left(x \right)} - 2 = 0$$
- this is the simplest trigonometric equation
We get:
$$c \sin{\left(x \right)} = 2$$
The equation is transformed to
$$\sin{\left(x \right)} = \frac{2}{c}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{c} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{c} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{c} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{c} \right)} + \pi$$
, where n - is a integer
$$c \sin{\left(x \right)} - 2 = 0$$
- this is the simplest trigonometric equation
Move -2 to right part of the equation
with the change of sign in -2
We get:
$$c \sin{\left(x \right)} = 2$$
Divide both parts of the equation by c
The equation is transformed to
$$\sin{\left(x \right)} = \frac{2}{c}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{c} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{c} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{c} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{c} \right)} + \pi$$
, where n - is a integer
The graph
Rapid solution
[src]
/ /2\\ / /2\\
x1 = pi - re|asin|-|| - I*im|asin|-||
\ \c// \ \c//
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + \pi$$
/ /2\\ / /2\\
x2 = I*im|asin|-|| + re|asin|-||
\ \c// \ \c//
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}$$
x2 = re(asin(2/c)) + i*im(asin(2/c))
Sum and product of roots
[src]
sum
/ /2\\ / /2\\ / /2\\ / /2\\
pi - re|asin|-|| - I*im|asin|-|| + I*im|asin|-|| + re|asin|-||
\ \c// \ \c// \ \c// \ \c//
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + \pi\right)$$
=
pi
$$\pi$$
product
/ / /2\\ / /2\\\ / / /2\\ / /2\\\ |pi - re|asin|-|| - I*im|asin|-|||*|I*im|asin|-|| + re|asin|-||| \ \ \c// \ \c/// \ \ \c// \ \c///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + \pi\right)$$
=
/ / /2\\ / /2\\\ / / /2\\ / /2\\\ -|I*im|asin|-|| + re|asin|-|||*|-pi + I*im|asin|-|| + re|asin|-||| \ \ \c// \ \c/// \ \ \c// \ \c///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - \pi\right)$$
-(i*im(asin(2/c)) + re(asin(2/c)))*(-pi + i*im(asin(2/c)) + re(asin(2/c)))