Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=-100
-
Equation 2x^2-3x+1=0
-
Equation -7*x=4
-
Equation 10x-2(4x-5)=2x+10
- Express {x} in terms of y where:
- 4*x-4*y=-19
- 5*x-4*y=14
- -16*x+18*y=9
- 4*x-1*y=12
-
Identical expressions
- five (one +cosx)= zero
- 5(1 plus co sinus of e of x) equally 0
- five (one plus co sinus of e of x) equally zero
- 51+cosx=0
- 5(1+cosx)=O
-
Similar expressions
- 5(1-cosx)=0
5(1+cosx)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$5 \left(\cos{\left(x \right)} + 1\right) = 0$$
- this is the simplest trigonometric equation
We get:
$$5 \left(\cos{\left(x \right)} + 1\right) - 5 = -5$$
The equation is transformed to
$$\cos{\left(x \right)} = -1$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$x = \pi n + \pi$$
$$x = \pi n$$
, where n - is a integer
$$5 \left(\cos{\left(x \right)} + 1\right) = 0$$
- this is the simplest trigonometric equation
Move 5 to right part of the equation
with the change of sign in 5
We get:
$$5 \left(\cos{\left(x \right)} + 1\right) - 5 = -5$$
Divide both parts of the equation by 5
The equation is transformed to
$$\cos{\left(x \right)} = -1$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$x = \pi n + \pi$$
$$x = \pi n$$
, where n - is a integer
Numerical answer
[src]
x1 = -53.4070745786761
x2 = -47.1238901083229
x3 = 9.42477748794163
x4 = -65.9734461969855
x5 = -59.6902606928653
x6 = 15.7079634518075
x7 = 47.123889410773
x8 = 28.2743343711514
x9 = 3.1415922548952
x10 = 40.8407045848602
x11 = -72.2566311847166
x12 = 59.6902600526626
x13 = 21.9911485852059
x14 = -9.4247781365785
x15 = -28.2743337069329
x16 = -34.5575188899093
x17 = -15.707962774825
x18 = 59.6902606104322
x19 = 34.5575197055812
x20 = -91.1061864815274
x21 = -21.9911485864417
x22 = 78.5398166181283
x23 = 91.1061865667532
x24 = -9.42477744529557
x25 = -53.4070745963886
x26 = 3.14159306054457
x27 = -65.9734453607004
x28 = 91.1061873718352
x29 = 65.9734460390947
x30 = 97.3893717959212
x31 = 28.2743338651796
x32 = -34.5575196658297
x33 = -97.3893717476911
x34 = -40.8407049008781
x35 = -28.2743340989896
x36 = -15.7079635641079
x37 = 59.6902599104079
x38 = 72.2566315166773
x39 = -28.2743343914215
x40 = -9.42477752082051
x41 = 34.5575190219169
x42 = 21.9911480932338
x43 = -3.14159217367683
x44 = -21.9911490521325
x45 = 72.2566306985
x46 = 72.2566310277176
x47 = -59.6902599212271
x48 = 15.7079627593774
x49 = -15.7079632965989
x50 = 65.9734452390837
x51 = 40.8407042062167
x52 = -1127.83176318906
x53 = -84.8230020565447
x54 = -84.8230012511693
x55 = 53.4070746418597
x56 = 84.8230013636028
x57 = 47.1238902162437
x58 = 97.389372581711
x59 = -40.8407040952604
x60 = -91.106187265474
x61 = 84.8230021335997
x62 = -47.1238893275319
x63 = 78.5398168562347
x64 = 9.42477826738203
x65 = -53.407075294995
x66 = 15.7079629803241
x67 = 78.5398161804942
x68 = -97.3893724533348
x69 = 15.707963957033
x70 = -72.2566308657983
x71 = 40.8407045792514
x72 = -97.3893716284562
x73 = -78.5398160472843
x74 = 28.2743335663982
x75 = 21.9911489072506
x76 = 40.8407049800347
x77 = -78.5398168194507
x78 = 65.9734457529812
x79 = -21.991148226056
x80 = -72.2566315419804
x81 = -40.8407049290801
x82 = 34.5575195449229
x83 = -3.14159295109225
x84 = 53.407075424589
x85 = -59.6902604578012
x86 = -65.9734457649277
x86 = -65.9734457649277