Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(4*x)=-sqrt(2)/2
- Equation sin3x+sinx-sin2x=2cos^2x-2cosx
- Equation sin(x)=7//2pi
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Equation 9x^2=27x
- Express {x} in terms of y where:
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 4*x-16*y=6
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
- Canonical form:
- sin(x)
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Identical expressions
- sin(x)= seven //2pi
- sinus of (x) equally 7 divide by divide by 2 Pi
- sinus of (x) equally seven divide by divide by 2 Pi
- sinx=7//2pi
- sin(x)=7 divide by divide by 2pi
-
Similar expressions
- sinx=-1/2
- sin3x+sinx-sin2x=2cos^2x-2cosx
- 4sin^3(x)+3sinx+4sqrt(3)=4sqrt(3)*cos^2(x)
- sinx=7//2pi
sin(x)=7//2pi equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{7 \pi}{2}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\sin{\left(x \right)} = \frac{7 \pi}{2}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
True
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
Rapid solution
[src]
/ /7*pi\\ / /7*pi\\
x1 = pi - re|asin|----|| - I*im|asin|----||
\ \ 2 // \ \ 2 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}$$
/ /7*pi\\ / /7*pi\\
x2 = I*im|asin|----|| + re|asin|----||
\ \ 2 // \ \ 2 //
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}$$
x2 = re(asin(7*pi/2)) + i*im(asin(7*pi/2))
Sum and product of roots
[src]
sum
/ /7*pi\\ / /7*pi\\ / /7*pi\\ / /7*pi\\
pi - re|asin|----|| - I*im|asin|----|| + I*im|asin|----|| + re|asin|----||
\ \ 2 // \ \ 2 // \ \ 2 // \ \ 2 //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / /7*pi\\ / /7*pi\\\ / / /7*pi\\ / /7*pi\\\ |pi - re|asin|----|| - I*im|asin|----|||*|I*im|asin|----|| + re|asin|----||| \ \ \ 2 // \ \ 2 /// \ \ \ 2 // \ \ 2 ///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}\right)$$
=
/ / /7*pi\\ / /7*pi\\\ / / /7*pi\\ / /7*pi\\\ -|I*im|asin|----|| + re|asin|----|||*|-pi + I*im|asin|----|| + re|asin|----||| \ \ \ 2 // \ \ 2 /// \ \ \ 2 // \ \ 2 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{7 \pi}{2} \right)}\right)}\right)$$
-(i*im(asin(7*pi/2)) + re(asin(7*pi/2)))*(-pi + i*im(asin(7*pi/2)) + re(asin(7*pi/2)))
Numerical answer
[src]
x1 = 1.5707963267949 + 3.08856581244844*i
x2 = 1.5707963267949 - 3.08856581244844*i
x2 = 1.5707963267949 - 3.08856581244844*i