Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-1)/(5-x)=2/9
-
Equation x^2-3x-4=0
- Equation x^2-4x-45=0
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Equation (x^2-9)^2+(x^2-2*x-15)^2=0
- Express {x} in terms of y where:
- (x^2+y^2-1)^3-x^2*y^3=0
- -14*x-3*y=-5
- -2*x+1*y=-8
- -2*x-1*y=-8
- Integral of d{x}:
- sinx/4
- Derivative of:
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sinx/4
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Identical expressions
- sinx/ four =-sqrt two /2
- sinus of x divide by 4 equally minus square root of 2 divide by 2
- sinus of x divide by four equally minus square root of two divide by 2
- sinx/4=-√2/2
- sinx divide by 4=-sqrt2 divide by 2
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Similar expressions
- sin(x/4-pi/8)=0
- cos(2*x)*(2*cos(7*x))+cos(5*x+pi)=-sqrt(2)/2
- sinx/4=+sqrt2/2
- 2*sin(x/4-pi/3)=(3)^(1/2)
- cos(x)+sqrt((2-sqrt2)/2)*(sin(x)+1)=0
- cos*((pi*(2*x+6))/4)=-(sqrt2/2)
- cos(pi(4×x+108)/4)=-sqrt(2)/2
- sin(x/4)=1/2sqrt(5,5/30)
- 6*sin(x/4-pi/12)-6=0
sinx/4=-sqrt2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ sin(x) -\/ 2 ------ = ------- 4 2
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Detail solution
Given the equation
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = - 2 \sqrt{2}$$
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.
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/4
The equation is transformed to
$$\sin{\left(x \right)} = - 2 \sqrt{2}$$
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.
Sum and product of roots
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sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ 0 + pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 // + - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 //
$$\left(0 + \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)\right) - \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ 1*\pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\- re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 ///
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) 1 \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ -\I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)$$
-(i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))*(pi + i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))
Rapid solution
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/ / ___\\ / / ___\\ x1 = pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 //
$$x_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}$$
/ / ___\\ / / ___\\ x2 = - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 //
$$x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}$$
Numerical answer
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x1 = 4.71238898038469 - 1.70004220705667*i
x2 = -1.5707963267949 + 1.70004220705667*i
x2 = -1.5707963267949 + 1.70004220705667*i
The graph