Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-2)^2*(x-3)=12*(x-2)
-
Equation 3x=28-x
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Equation x^4=-16
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Equation cos(x)=1/sqrt(2)
- Express {x} in terms of y where:
- -2*x+18*y=13
- -2*x-7*y=-16
- -8*x-16*y=-1
- -3*x+17*y=-5
- Derivative of:
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cos(x)
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1/sqrt(2)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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Identical expressions
- cos(x)= one /sqrt(two)
- co sinus of e of (x) equally 1 divide by square root of (2)
- co sinus of e of (x) equally one divide by square root of (two)
- cos(x)=1/√(2)
- cosx=1/sqrt2
- cos(x)=1 divide by sqrt(2)
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Similar expressions
- (-2cos^2x-sinx-1)log0,5(-0,8cosx)=0
- 0.3536=1/(sqrt((2*143*700*pi*x/(10*10^9))^2+4))
- sqrt((1+(x*7.5*(10^3)*1*(10^(-9)))^2)/((1-(x*7.5*(10^3)*1*(10^(-9)))^2)^2+(4*x*7.5*(10^3)*1*(10^(-9)))^2))=1/(sqrt(2))
- 2sinx^2+1,5sin2x-3cos(x^2)=1
- cos(2*x-pi/4)=1/(sqrt(2))
- cosx=1/sqrt(2)
cos(x)=1/sqrt(2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{1}{\sqrt{2}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{1}{\sqrt{2}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
7*pi
x2 = ----
4
$$x_{2} = \frac{7 \pi}{4}$$
x2 = 7*pi/4
Sum and product of roots
[src]
sum
pi 7*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{7 \pi}{4}$$
=
2*pi
$$2 \pi$$
product
pi 7*pi --*---- 4 4
$$\frac{\pi}{4} \frac{7 \pi}{4}$$
=
2 7*pi ----- 16
$$\frac{7 \pi^{2}}{16}$$
7*pi^2/16
Numerical answer
[src]
x1 = 95.0331777710912
x2 = 32.2013246992954
x3 = -182.997772071605
x4 = -49.4800842940392
x5 = 69.9004365423729
x6 = 38.484510006475
x7 = -13.3517687777566
x8 = -93.4623814442964
x9 = -63.6172512351933
x10 = 68.329640215578
x11 = -44.7676953136546
x12 = 76.1836218495525
x13 = -101.316363078271
x14 = -18.0641577581413
x15 = 49.4800842940392
x16 = 24.3473430653209
x17 = 36.9137136796801
x18 = 30.6305283725005
x19 = 5.49778714378214
x20 = 51.0508806208341
x21 = 43.1968989868597
x22 = 11.7809724509617
x23 = -57.3340659280137
x24 = -51.0508806208341
x25 = -87.1791961371168
x26 = 99.7455667514759
x27 = 80.8960108299372
x28 = -69.9004365423729
x29 = -95.0331777710912
x30 = 44.7676953136546
x31 = -99.7455667514759
x32 = 13.3517687777566
x33 = -7.06858347057703
x34 = 87.1791961371168
x35 = -32.2013246992954
x36 = -25.9181393921158
x37 = 74.6128255227576
x38 = 93.4623814442964
x39 = -68.329640215578
x40 = -24.3473430653209
x41 = -5.49778714378214
x42 = 0.785398163397448
x43 = 82.4668071567321
x44 = -82.4668071567321
x45 = 25.9181393921158
x46 = -162.577419823272
x47 = -351.072979038659
x48 = 57.3340659280137
x49 = -30.6305283725005
x50 = -36.9137136796801
x51 = 18.0641577581413
x52 = 55.7632696012188
x53 = -0.785398163397448
x54 = -43.1968989868597
x55 = -80.8960108299372
x56 = 88.7499924639117
x57 = -55.7632696012188
x58 = 62.0464549083984
x59 = -62.0464549083984
x60 = -38.484510006475
x61 = -88.7499924639117
x62 = 19.6349540849362
x63 = -76.1836218495525
x64 = -19.6349540849362
x65 = 7.06858347057703
x66 = -74.6128255227576
x67 = 63.6172512351933
x68 = -11.7809724509617
x68 = -11.7809724509617
The graph