Mister Exam
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- Equation:
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Equation x^2+11*x+30=0
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Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
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Equation (|3*x-9|)-(|x+2|)=7
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Equation 3(x-1)-6=0
- Express {x} in terms of y where:
- 15*x-2*y=14
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Identical expressions
- tan(pi*(x- three))/ six = one
- tangent of ( Pi multiply by (x minus 3)) divide by 6 equally 1
- tangent of ( Pi multiply by (x minus three)) divide by six equally one
- tan(pi(x-3))/6=1
- tanpix-3/6=1
- tan(pi*(x-3)) divide by 6=1
-
Similar expressions
- tan(pi*(x+3))/6=1
- tanpi*(x-3)/6=1
tan(pi*(x-3))/6=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
tan(pi*(x - 3))
--------------- = 1
6
$$\frac{\tan{\left(\pi \left(x - 3\right) \right)}}{6} = 1$$
Detail solution
Given the equation
$$\frac{\tan{\left(\pi \left(x - 3\right) \right)}}{6} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(\pi x \right)} = 6$$
This equation is transformed to
$$\pi x = \pi n + \operatorname{atan}{\left(6 \right)}$$
Or
$$\pi x = \pi n + \operatorname{atan}{\left(6 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{\pi n + \operatorname{atan}{\left(6 \right)}}{\pi}$$
$$\frac{\tan{\left(\pi \left(x - 3\right) \right)}}{6} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/6
The equation is transformed to
$$\tan{\left(\pi x \right)} = 6$$
This equation is transformed to
$$\pi x = \pi n + \operatorname{atan}{\left(6 \right)}$$
Or
$$\pi x = \pi n + \operatorname{atan}{\left(6 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{\pi n + \operatorname{atan}{\left(6 \right)}}{\pi}$$
Sum and product of roots
[src]
sum
atan(6) ------- pi
$$\frac{\operatorname{atan}{\left(6 \right)}}{\pi}$$
=
atan(6) ------- pi
$$\frac{\operatorname{atan}{\left(6 \right)}}{\pi}$$
product
atan(6) ------- pi
$$\frac{\operatorname{atan}{\left(6 \right)}}{\pi}$$
=
atan(6) ------- pi
$$\frac{\operatorname{atan}{\left(6 \right)}}{\pi}$$
atan(6)/pi
Rapid solution
[src]
atan(6)
x1 = -------
pi
$$x_{1} = \frac{\operatorname{atan}{\left(6 \right)}}{\pi}$$
x1 = atan(6)/pi