Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x-6/x=-1
-
Equation x=x/2+1
-
Equation 5-2x=11-7(x+2)
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Equation x^2=6
- Express {x} in terms of y where:
- 14*x-16*y=-3
- 17*x-20*y=6
- 10*x-19*y=3
- -2*x-1*y=-8
-
Identical expressions
- tan(pi*x/ six)=sqrt(three / three)
- tangent of ( Pi multiply by x divide by 6) equally square root of (3 divide by 3)
- tangent of ( Pi multiply by x divide by six) equally square root of (three divide by three)
- tan(pi*x/6)=√(3/3)
- tan(pix/6)=sqrt(3/3)
- tanpix/6=sqrt3/3
- tan(pi*x divide by 6)=sqrt(3 divide by 3)
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Similar expressions
- tg((pi(4x-21))/6)=(sqrt(3))/3
- tg(x-(pi/4))=-(sqrt3)/3
- tan5(x)=-sqrt(3)/3
- (x^2-(a+4)*x+2*a+4)*(cot(x))/(pi*x/3-sqrt(3)/3)=0
tan(pi*x/6)=sqrt(3/3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi*x\ ___ tan|----| = \/ 1 \ 6 /
$$\tan{\left(\frac{\pi x}{6} \right)} = \sqrt{1}$$
Detail solution
Given the equation
$$\tan{\left(\frac{\pi x}{6} \right)} = \sqrt{1}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{6} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$\frac{\pi x}{6} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{6}$$
we get the answer:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{4}\right)}{\pi}$$
$$\tan{\left(\frac{\pi x}{6} \right)} = \sqrt{1}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{6} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$\frac{\pi x}{6} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{6}$$
we get the answer:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{4}\right)}{\pi}$$
Sum and product of roots
[src]
sum
3/2
$$\frac{3}{2}$$
=
3/2
$$\frac{3}{2}$$
product
3/2
$$\frac{3}{2}$$
=
3/2
$$\frac{3}{2}$$
3/2
Numerical answer
[src]
x1 = -34.5
x2 = 37.5
x3 = -28.5
x4 = 1.5
x5 = 79.5
x6 = -4.5
x7 = 49.5
x8 = 97.5
x9 = -64.5
x10 = 103.5
x11 = 73.5
x12 = -22.5
x13 = 19.5
x14 = 91.5
x15 = 67.5
x16 = 7.5
x17 = -46.5
x18 = -58.5
x19 = -94.5
x20 = -100.5
x21 = 43.5
x22 = 13.5
x23 = 61.5
x24 = 31.5
x25 = -70.5
x26 = 55.5
x27 = 25.5
x28 = 85.5
x29 = -82.5
x30 = -52.5
x31 = -10.5
x32 = -16.5
x33 = -88.5
x34 = -40.5
x35 = -76.5
x35 = -76.5