Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation 5*x^2-45=0
-
Equation x+4=-1
-
Equation 16*x^3+8*x^2+x=0
-
Equation -7x=4
- Express {x} in terms of y where:
- -16*x-10*y=4
- -3*x-10*y=1
- 7*x-19*y=17
- 20*x-9*y=-8
- Derivative of:
-
cos2x
- Integral of d{x}:
-
cos2x
- Graphing y =:
- cos2x
-
Identical expressions
- cos2x= one
- co sinus of e of 2x equally 1
- co sinus of e of 2x equally one
-
Similar expressions
- cos(2*x)+cos(8*x)-cos(6*x)=1
- cos(2*x)+5*sin(x)+2=0
- 5cos^2*x+8*cos(x)=4
- sin^2(x)+sin(2x)-3cos^2(x)=0
cos2x=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(2 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$2 x = \pi n$$
$$2 x = \pi n - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2}$$
$$\cos{\left(2 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$2 x = \pi n$$
$$2 x = \pi n - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2}$$
Numerical answer
[src]
x1 = -31.4159267051849
x2 = 34.5575190304759
x3 = -18.8495561207399
x4 = 18.8495554002244
x5 = 25.1327414478072
x6 = 75.3982241944528
x7 = -18.8495556944209
x8 = 31.4159271479423
x9 = -62.8318528379059
x10 = -37.6991118771514
x11 = 3.14159244884412
x12 = -25.132741632083
x13 = 9.42477859080277
x14 = 87.9645943357576
x15 = 91.1061871583643
x16 = -53.4070752836338
x17 = -91.106187201329
x18 = 47.123889589354
x19 = 69.1150385885879
x20 = -69.1150386737158
x21 = 3.14159287686128
x22 = -65.9734457650176
x23 = 0.0
x24 = -9.42477812668337
x25 = 91.1061867314459
x26 = 53.4070753627408
x27 = -40.8407046898283
x28 = -50.2654822953391
x29 = -6371388.6625218
x30 = -12.5663703661411
x31 = -6.28318513794069
x32 = -47.123890151099
x33 = -59.6902604576401
x34 = -81.6814090380061
x35 = 97.3893727097471
x36 = 37.6991120192083
x37 = 50.2654824463473
x38 = 78.5398161878405
x39 = -25.132741473063
x40 = 15.7079634406648
x41 = -15.7079632965264
x42 = 69.1150381602162
x43 = 62.8318524523063
x44 = 18.8495556796107
x45 = -3.14159311568248
x46 = -87.9645943587732
x47 = -84.82300141007
x48 = 59.6902605976901
x49 = 84.8230014093114
x50 = -47.1238900492539
x51 = -75.3982238620294
x52 = 28.2743338652012
x53 = -34.5575189426108
x54 = 100.530964766599
x55 = 62.8318528326557
x56 = -78.5398160958028
x57 = 81.6814091761104
x58 = 43.982297169427
x59 = -106.814150357553
x60 = 6.28318528425126
x61 = -84.8230018263493
x62 = -31.4159267959754
x63 = -72.2566308741333
x64 = -21.9911485864515
x65 = 56.5486676091327
x66 = -62.8318532583801
x67 = -100.530964672522
x68 = -69.1150386253436
x69 = -3.14159289677385
x70 = 97.3893725148693
x71 = 25.1327410188866
x72 = -43.9822971745789
x73 = 31.4159267865366
x74 = 40.840703919946
x75 = 53.4070756765307
x76 = -94.2477794529919
x77 = -12.5663700417108
x78 = 9.42477821024198
x79 = 65.9734457528975
x80 = -56.5486675191652
x81 = -97.3893724403711
x82 = 12.5663704518704
x83 = -1734.15914475848
x84 = -28.2743337166085
x85 = -40.8407042660168
x86 = 94.2477796093525
x87 = 84.8230010166547
x88 = 75.3982239388525
x89 = -91.1061872003049
x90 = 40.8407042560881
x91 = 72.256631027719
x92 = 47.123890018392
x93 = 21.9911485851964
x94 = -34.5575189701076
x94 = -34.5575189701076
The graph