Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation k^2+4=0
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Equation 2x^2+4x-4=x^2+5x+(-3+x^2)
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Equation sqrt(2)*cos(x/2)+1=0
- Equation 1+sinx/n=7
- Express {x} in terms of y where:
- -14*x+19*y=-3
- -11*x+10*y=-9
- -14*x+1*y=3
- 10*x+9*y=-4
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Identical expressions
- one +sinx/n= seven
- 1 plus sinus of x divide by n equally 7
- one plus sinus of x divide by n equally seven
- 1+sinx divide by n=7
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Similar expressions
- 1-sinx/n=7
1+sinx/n=7 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$1 + \frac{\sin{\left(x \right)}}{n} = 7$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = 6 n$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(6 n \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(6 n \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(6 n \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(6 n \right)} + \pi$$
, where n - is a integer
$$1 + \frac{\sin{\left(x \right)}}{n} = 7$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/n
The equation is transformed to
$$\sin{\left(x \right)} = 6 n$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(6 n \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(6 n \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(6 n \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(6 n \right)} + \pi$$
, where n - is a integer
The graph
Rapid solution
[src]
x1 = pi - re(asin(6*n)) - I*im(asin(6*n))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + \pi$$
x2 = I*im(asin(6*n)) + re(asin(6*n))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)}$$
x2 = re(asin(6*n)) + i*im(asin(6*n))
Sum and product of roots
[src]
sum
pi - re(asin(6*n)) - I*im(asin(6*n)) + I*im(asin(6*n)) + re(asin(6*n))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + \pi\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(6*n)) - I*im(asin(6*n)))*(I*im(asin(6*n)) + re(asin(6*n)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + \pi\right)$$
=
-(I*im(asin(6*n)) + re(asin(6*n)))*(-pi + I*im(asin(6*n)) + re(asin(6*n)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(6 n \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(6 n \right)}\right)} - \pi\right)$$
-(i*im(asin(6*n)) + re(asin(6*n)))*(-pi + i*im(asin(6*n)) + re(asin(6*n)))