Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=11
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Equation log(4/(7-x))/log(x^2)=5
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Equation sin(2*x)=-1
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Equation -2*x/(x^2+1)^2=0
- Express {x} in terms of y where:
- -14*x-16*y=14
- 16*x-17*y=-9
- -14*x-3*y=-5
- -16*x-20*y=6
- Sum of series:
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1/2
- Integral of d{x}:
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1/2
- Derivative of:
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1/2
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Identical expressions
- sinx*cospi/ eight +cosx*sinpi/ eight = one / two
- sinus of x multiply by co sinus of e of Pi divide by 8 plus co sinus of e of x multiply by sinus of Pi divide by 8 equally 1 divide by 2
- sinus of x multiply by co sinus of e of Pi divide by eight plus co sinus of e of x multiply by sinus of Pi divide by eight equally one divide by two
- sinxcospi/8+cosxsinpi/8=1/2
- sinx*cospi divide by 8+cosx*sinpi divide by 8=1 divide by 2
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Similar expressions
- sinx*cospi/8-cosx*sinpi/8=1/2
sinx*cospi/8+cosx*sinpi/8=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(x)*cos(pi) cos(x)*sin(pi)
-------------- + -------------- = 1/2
8 8
$$\frac{\sin{\left(\pi \right)} \cos{\left(x \right)}}{8} + \frac{\sin{\left(x \right)} \cos{\left(\pi \right)}}{8} = \frac{1}{2}$$
Detail solution
Given the equation
$$\frac{\sin{\left(\pi \right)} \cos{\left(x \right)}}{8} + \frac{\sin{\left(x \right)} \cos{\left(\pi \right)}}{8} = \frac{1}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = -4$$
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.
$$\frac{\sin{\left(\pi \right)} \cos{\left(x \right)}}{8} + \frac{\sin{\left(x \right)} \cos{\left(\pi \right)}}{8} = \frac{1}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1/8
The equation is transformed to
$$\sin{\left(x \right)} = -4$$
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
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x1 = pi + I*im(asin(4)) + re(asin(4))
$$x_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}$$
x2 = -re(asin(4)) - I*im(asin(4))
$$x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}$$
x2 = -re(asin(4)) - i*im(asin(4))
Sum and product of roots
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sum
pi + I*im(asin(4)) + re(asin(4)) + -re(asin(4)) - I*im(asin(4))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi + I*im(asin(4)) + re(asin(4)))*(-re(asin(4)) - I*im(asin(4)))
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
=
-(I*im(asin(4)) + re(asin(4)))*(pi + I*im(asin(4)) + re(asin(4)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
-(i*im(asin(4)) + re(asin(4)))*(pi + i*im(asin(4)) + re(asin(4)))
Numerical answer
[src]
x1 = 4.71238898038469 - 2.06343706889556*i
x2 = -1.5707963267949 + 2.06343706889556*i
x2 = -1.5707963267949 + 2.06343706889556*i