Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (-5x+3)*(-x+6)=0
- Equation sin(x)=a
- Equation f*(x)=3
- Equation z^3=-i
- Express {x} in terms of y where:
- -8*x+14*y=5
- 17*x+7*y=-6
- -11*x-14*y=6
- -18*x-8*y=-5
- 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)=a
- sinus of (x) equally a
- sinx=a
-
Similar expressions
- sinx=a
sin(x)=a equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = a$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(a \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(a \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = a$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(a \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(a \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi$$
, where n - is a integer
The graph
Sum and product of roots
[src]
sum
pi - re(asin(a)) - I*im(asin(a)) + I*im(asin(a)) + re(asin(a))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(a)) - I*im(asin(a)))*(I*im(asin(a)) + re(asin(a)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi\right)$$
=
-(I*im(asin(a)) + re(asin(a)))*(-pi + I*im(asin(a)) + re(asin(a)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} - \pi\right)$$
-(i*im(asin(a)) + re(asin(a)))*(-pi + i*im(asin(a)) + re(asin(a)))
Rapid solution
[src]
x1 = pi - re(asin(a)) - I*im(asin(a))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi$$
x2 = I*im(asin(a)) + re(asin(a))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}$$
x2 = re(asin(a)) + i*im(asin(a))