Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
-
Equation x^2+8*x+15=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Graphing y =:
- cos(6x)
- Integral of d{x}:
-
cos(6x)
- Derivative of:
- cos(6x)
- Limit of the function:
-
sqrt(2)/2
- sqrt(2)/2
-
Identical expressions
- cos(6x)=sqrt(two)/ two
- co sinus of e of (6x) equally square root of (2) divide by 2
- co sinus of e of (6x) equally square root of (two) divide by two
- cos(6x)=√(2)/2
- cos6x=sqrt2/2
- cos(6x)=sqrt(2) divide by 2
-
Similar expressions
- cos(6*x)-cos(8*x)=1-cos(2*x)
- cos(2*x)+cos(8*x)-cos(6*x)=1
- sin((-3)*x+pi/6)=(-sqrt(2))/2
- cos6x=-sqrt(3/2)
cos(6x)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(6 x \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$6 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$6 x = \pi n + \frac{\pi}{4}$$
$$6 x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$6$$
we get the answer:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{8}$$
$$\cos{\left(6 x \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$6 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$6 x = \pi n + \frac{\pi}{4}$$
$$6 x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$6$$
we get the answer:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{8}$$
Sum and product of roots
[src]
sum
pi 7*pi -- + ---- 24 24
$$\frac{\pi}{24} + \frac{7 \pi}{24}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
pi 7*pi --*---- 24 24
$$\frac{\pi}{24} \frac{7 \pi}{24}$$
=
2 7*pi ----- 576
$$\frac{7 \pi^{2}}{576}$$
7*pi^2/576
Rapid solution
[src]
pi
x1 = --
24
$$x_{1} = \frac{\pi}{24}$$
7*pi
x2 = ----
24
$$x_{2} = \frac{7 \pi}{24}$$
x2 = 7*pi/24
Numerical answer
[src]
x1 = -15.8388629618485
x2 = -21.860248881229
x3 = -67.9369411338793
x4 = 42.0188017417635
x5 = 39.9244066393703
x6 = 20.0276531666349
x7 = -79.717913584841
x8 = -90.9752872602044
x9 = 10.3410758180664
x10 = -86.0010988920206
x11 = -4.05789051088682
x12 = 81.550509299435
x13 = -81.8123086872342
x14 = -57.7267650097125
x15 = -50.1345827635371
x16 = -55.6323699073193
x17 = 32.332224393195
x18 = 37.8300115369771
x19 = -41.7570023539643
x20 = 66.1043454192852
x21 = 92.2842841992002
x22 = 24.2164433714213
x23 = 100.661864608773
x24 = 12.6972703082587
x25 = -72.1257313386657
x26 = 100.400065220974
x27 = -18.7186562276392
x28 = 46.2075919465499
x29 = -33.6412213321907
x30 = 86.0010988920206
x31 = 96.4730744039866
x32 = 2.22529479629277
x33 = -59.8211601121056
x34 = -9.29387826686981
x35 = 17.9332580642417
x36 = -28.1434341884086
x37 = 72.1257313386657
x38 = -94.1168799137942
x39 = 28.1434341884086
x40 = -65.8425460314861
x41 = 5.36688744988256
x42 = -19.7658537788358
x43 = -83.9067037896274
x44 = 6.15228561328001
x45 = 98.3056701185806
x46 = 56.4177680707167
x47 = 76.3145215434521
x48 = 25.0018415348188
x49 = 61.9155552144988
x50 = 26.3108384738145
x51 = 88.0954939944138
x52 = -87.8336946066146
x53 = 90.189889096807
x54 = 52.2289778659303
x55 = -92.022484811401
x56 = -45.9457925587507
x57 = 94.1168799137942
x58 = -26.0490390860154
x59 = -31.2850268419984
x60 = 30.2378292908018
x61 = 48.3019870489431
x62 = -11.6500727570621
x63 = -23.9546439836222
x64 = -63.7481509290929
x65 = -6.15228561328001
x66 = -35.7356164345839
x67 = -43.8513974563575
x68 = 68.1987405216784
x69 = -77.6235184824478
x70 = -89.9280897090078
x71 = 111.919238284136
x72 = -61.9155552144988
x73 = 0.130899693899575
x74 = 58.773962560909
x75 = 8.24668071567321
x76 = -70.0313362362725
x77 = -1.96349540849362
x78 = -110.086642569542
x79 = 44.1131968441567
x80 = 22.9074464324256
x81 = 78.4089166458453
x82 = -13.7444678594553
x83 = 83.9067037896274
x84 = -37.8300115369771
x85 = -99.6146670575764
x86 = 22.1220482690281
x87 = 10.6028752058656
x88 = 15.8388629618485
x89 = 50.1345827635371
x90 = 96.2112750161874
x91 = 74.2201264410589
x92 = -48.0401876611439
x93 = 54.3233729683235
x94 = 70.2931356240716
x95 = 64.009950316892
x95 = 64.009950316892