Mister Exam
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How to use it?
- Equation:
-
Equation cos4x=0
-
Equation ctg(x)=0
- Equation s-0,522s=3,585
- Equation (x^2+20)/(x^2-4)=(x-3)/(x+2)+(6)/(x-2)
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- Derivative of:
-
cos4x
- Integral of d{x}:
-
cos4x
- Canonical form:
- cos4x
-
Identical expressions
- cos4x= zero
- co sinus of e of 4x equally 0
- co sinus of e of 4x equally zero
- cos4x=O
-
Similar expressions
- sin((2*x+2*pi)/3)*cos((4*x+pi)/3)-cos(2*x)=sin(x)^2/cos(-(-pi)/3)
- 4*cos^4x+9*cos^2x-1=0
cos4x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(4 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(4 x \right)} = 0$$
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{acos}{\left(0 \right)}$$
$$4 x = 2 \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$4 x = 2 \pi n + \frac{\pi}{2}$$
$$4 x = 2 \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{8}$$
$$\cos{\left(4 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(4 x \right)} = 0$$
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{acos}{\left(0 \right)}$$
$$4 x = 2 \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$4 x = 2 \pi n + \frac{\pi}{2}$$
$$4 x = 2 \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{8}$$
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 8 8
$$\left(\frac{\pi}{8}\right) + \left(\frac{3 \pi}{8}\right)$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi 3*pi -- * ---- 8 8
$$\left(\frac{\pi}{8}\right) * \left(\frac{3 \pi}{8}\right)$$
=
2 3*pi ----- 64
$$\frac{3 \pi^{2}}{64}$$
Rapid solution
[src]
pi
x_1 = --
8
$$x_{1} = \frac{\pi}{8}$$
3*pi
x_2 = ----
8
$$x_{2} = \frac{3 \pi}{8}$$
Numerical answer
[src]
x1 = 96.9966731795849
x2 = -100.138265833175
x3 = -75.7909227678538
x4 = -60.0829594999048
x5 = 40.4480054149686
x6 = 92.2842841992002
x7 = 66.3661448070844
x8 = 38.0918109247762
x9 = -61.6537558266997
x10 = -9.8174770424681
x11 = 96.2112750161874
x12 = 70.2931356240716
x13 = -64.009950316892
x14 = 30.2378292908018
x15 = -31.8086256175967
x16 = -13.7444678594553
x17 = -96.9966731795849
x18 = 67.9369411338793
x19 = 89.9280897090078
x20 = 104.850654813559
x21 = -68.7223392972767
x22 = 93.8550805259951
x23 = 74.2201264410589
x24 = -97.7820713429823
x25 = -17.6714586764426
x26 = 56.1559686829176
x27 = -87.5718952188155
x28 = 8.24668071567321
x29 = 31.8086256175967
x30 = 62.4391539900971
x31 = -1.96349540849362
x32 = 122.914812571701
x33 = 4.31968989868597
x34 = 84.4303025652257
x35 = -93.8550805259951
x36 = 27.8816348006094
x37 = 16.1006623496477
x38 = 45.9457925587507
x39 = -56.1559686829176
x40 = 64.009950316892
x41 = -79.717913584841
x42 = -75.0055246044563
x43 = 23.9546439836222
x44 = 100.138265833175
x45 = -34.164820107789
x46 = 49.872783375738
x47 = -49.872783375738
x48 = -10.6028752058656
x49 = 12.1736715326604
x50 = -89.9280897090078
x51 = 82.0741080750334
x52 = -53.7997741927252
x53 = -23.9546439836222
x54 = 42.0188017417635
x55 = -82.0741080750334
x56 = -39.6626072515711
x57 = 44.3749962319558
x58 = 26.3108384738145
x59 = -67.9369411338793
x60 = -45.9457925587507
x61 = 5.89048622548086
x62 = -42.0188017417635
x63 = -20.0276531666349
x64 = -71.8639319508665
x65 = 71.8639319508665
x66 = 0.392699081698724
x67 = -43.5895980685584
x68 = 20.0276531666349
x69 = 60.0829594999048
x70 = 78.1471172580461
x71 = 48.3019870489431
x72 = -2.74889357189107
x73 = 53.7997741927252
x74 = -35.7356164345839
x75 = -83.6449044018282
x76 = -65.5807466436869
x77 = -27.8816348006094
x78 = 88.3572933822129
x79 = 54.5851723561227
x80 = 34.164820107789
x81 = -5.89048622548086
x82 = 1.96349540849362
x83 = -16.1006623496477
x84 = -21.5984494934298
x85 = -86.0010988920206
x86 = -57.7267650097125
x87 = -38.0918109247762
x88 = -12.1736715326604
x89 = 22.3838476568273
x90 = 52.2289778659303
x91 = 9.8174770424681
x92 = -20.8130513300324
x93 = 86.0010988920206
x94 = -78.1471172580461
x94 = -78.1471172580461
The graph