Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4-3x^2-4=0
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Equation x^2-10x+25=0
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Equation x^2-9=(x+3)^2
- Equation x-y=0
- Express {x} in terms of y where:
- -12*x-8*y=13
- -4*x+19*y=-13
- -7*x+15*y=18
- 6*x-2*y=20
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
- Limit of the function:
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sin(x)
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Identical expressions
- sin(x)=- fifteen / fourteen
- sinus of (x) equally minus 15 divide by 14
- sinus of (x) equally minus fifteen divide by fourteen
- sinx=-15/14
- sin(x)=-15 divide by 14
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Similar expressions
- sin(x)=+15/14
- -15/(14*x*ln(2))=225/(14*(14-15x)*ln(2))
- sinx=-15/14
sin(x)=-15/14 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = - \frac{15}{14}$$
- 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.
$$\sin{\left(x \right)} = - \frac{15}{14}$$
- 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.
Sum and product of roots
[src]
sum
/ /15\\ / /15\\ / /15\\ / /15\\
pi + I*im|asin|--|| + re|asin|--|| + - re|asin|--|| - I*im|asin|--||
\ \14// \ \14// \ \14// \ \14//
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / /15\\ / /15\\\ / / /15\\ / /15\\\ |pi + I*im|asin|--|| + re|asin|--|||*|- re|asin|--|| - I*im|asin|--||| \ \ \14// \ \14/// \ \ \14// \ \14///
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}\right)$$
=
/ / /15\\ / /15\\\ / / /15\\ / /15\\\ -|I*im|asin|--|| + re|asin|--|||*|pi + I*im|asin|--|| + re|asin|--||| \ \ \14// \ \14/// \ \ \14// \ \14///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}\right)$$
-(i*im(asin(15/14)) + re(asin(15/14)))*(pi + i*im(asin(15/14)) + re(asin(15/14)))
Rapid solution
[src]
/ /15\\ / /15\\
x1 = pi + I*im|asin|--|| + re|asin|--||
\ \14// \ \14//
$$x_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}$$
/ /15\\ / /15\\
x2 = - re|asin|--|| - I*im|asin|--||
\ \14// \ \14//
$$x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{15}{14} \right)}\right)}$$
x2 = -re(asin(15/14)) - i*im(asin(15/14))
Numerical answer
[src]
x1 = 4.71238898038469 - 0.375750091349031*i
x2 = -1.5707963267949 + 0.375750091349031*i
x2 = -1.5707963267949 + 0.375750091349031*i