Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=-3
-
Equation 1/x^2+2/x-3=0
-
Equation 4=7-6(5x-1)
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Equation cos(x)=-sin(x)
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- -3*x+19*y=16
- Integral of d{x}:
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cos(x/3)
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-1/2
- Limit of the function:
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cos(x/3)
- -1/2
- Derivative of:
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cos(x/3)
- -1/2
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Identical expressions
- cos(x/ three)=- one / two
- co sinus of e of (x divide by 3) equally minus 1 divide by 2
- co sinus of e of (x divide by three) equally minus one divide by two
- cosx/3=-1/2
- cos(x divide by 3)=-1 divide by 2
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Similar expressions
- (x^2+1)/(9x-6)-1/(2-3x)=x/3
- (cos(x)/3*(1/100))*x-(5/2)=0
- cos(x/3)=+1/2
- 2cos^2x/3-5cosx/3-3=0
- -1/3*cos(x/3+pi/4)-cos=sin(x)
cos(x/3)=-1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(\frac{x}{3} \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$\frac{x}{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Or
$$\frac{x}{3} = \pi n + \frac{2 \pi}{3}$$
$$\frac{x}{3} = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n + 2 \pi$$
$$x_{2} = 3 \pi n - \pi$$
$$\cos{\left(\frac{x}{3} \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$\frac{x}{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Or
$$\frac{x}{3} = \pi n + \frac{2 \pi}{3}$$
$$\frac{x}{3} = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n + 2 \pi$$
$$x_{2} = 3 \pi n - \pi$$
Sum and product of roots
[src]
sum
2*pi + 4*pi
$$2 \pi + 4 \pi$$
=
6*pi
$$6 \pi$$
product
2*pi*4*pi
$$2 \pi 4 \pi$$
=
2 8*pi
$$8 \pi^{2}$$
8*pi^2
Numerical answer
[src]
x1 = 69.1150383789755
x2 = -50.2654824574367
x3 = 25.1327412287183
x4 = -175.929188601028
x5 = -69.1150383789755
x6 = -81.6814089933346
x7 = 50.2654824574367
x8 = 43.9822971502571
x9 = 87.9645943005142
x10 = -43.9822971502571
x11 = -6.28318530717959
x12 = 81.6814089933346
x13 = -62.8318530717959
x14 = 6.28318530717959
x15 = -43649.2883289766
x16 = -12.5663706143592
x17 = -31.4159265358979
x18 = 62.8318530717959
x19 = -87.9645943005142
x20 = -1840.97329500362
x21 = -25.1327412287183
x22 = 52602.8273917075
x23 = -6440.26493985908
x24 = 1407.43350880823
x25 = 100.530964914873
x26 = 31.4159265358979
x27 = 12.5663706143592
x28 = -100.530964914873
x28 = -100.530964914873
The graph