Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -x-2+3*(x-3)=3*(4-x)-3
-
Equation cos(x)+sin(x)=0
-
Equation 4x=24+x
-
Equation (x-7)^2=(9-x)^2
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 18*x-12*y=-20
- -19*x+1*y=0
- 14*x-13*y=-10
- Graphing y =:
-
sin2x
- Derivative of:
-
sin2x
- Sum of series:
- sin2x
-
Identical expressions
- sin2x= zero
- sinus of 2x equally 0
- sinus of 2x equally zero
- sin2x=O
-
Similar expressions
- -4*sin^2(x)-2*sin(x)+2=0
- 3sin(x)^2-3cos(x)-6sin(x)+2sin(2x)+3=0
- (sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)=0
- sin^2x-4sinx*cosx+3cos^2x=0
sin2x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(2 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(2 x \right)} = 0$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$2 x = 2 \pi n$$
$$2 x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \frac{\pi}{2}$$
$$\sin{\left(2 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(2 x \right)} = 0$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$2 x = 2 \pi n$$
$$2 x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \frac{\pi}{2}$$
Sum and product of roots
[src]
sum
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi 0*-- 2
$$0 \frac{\pi}{2}$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -50.2654824574367
x2 = 94.2477796076938
x3 = 64.4026493985908
x4 = 65.9734457253857
x5 = 20.4203522483337
x6 = -58.1194640914112
x7 = 92.6769832808989
x8 = -15.707963267949
x9 = 81.6814089933346
x10 = 6.28318530717959
x11 = -80.1106126665397
x12 = -483.805268652828
x13 = -31.4159265358979
x14 = 80.1106126665397
x15 = 78.5398163397448
x16 = -87.9645943005142
x17 = -72.2566310325652
x18 = -86.3937979737193
x19 = -37.6991118430775
x20 = -7.85398163397448
x21 = 31.4159265358979
x22 = 12.5663706143592
x23 = -45.553093477052
x24 = -17.2787595947439
x25 = -97.3893722612836
x26 = 72.2566310325652
x27 = 86.3937979737193
x28 = -119.380520836412
x29 = -39.2699081698724
x30 = -89.5353906273091
x31 = -6.28318530717959
x32 = 26.7035375555132
x33 = -20.4203522483337
x34 = -42.4115008234622
x35 = -9.42477796076938
x36 = -1.5707963267949
x37 = 23.5619449019235
x38 = -95.8185759344887
x39 = 36.1283155162826
x40 = 48.6946861306418
x41 = 58.1194640914112
x42 = 100.530964914873
x43 = 0.0
x44 = -65.9734457253857
x45 = -21.9911485751286
x46 = 7.85398163397448
x47 = 73.8274273593601
x48 = 95.8185759344887
x49 = 113.097335529233
x50 = -36.1283155162826
x51 = -23.5619449019235
x52 = -61.261056745001
x53 = 50.2654824574367
x54 = 43.9822971502571
x55 = 1.5707963267949
x56 = -53.4070751110265
x57 = -83.2522053201295
x58 = -51.8362787842316
x59 = -29.845130209103
x60 = 67.5442420521806
x61 = 15.707963267949
x62 = 28.2743338823081
x63 = -64.4026493985908
x64 = -73.8274273593601
x65 = 45.553093477052
x66 = -48.6946861306418
x67 = 21.9911485751286
x68 = 37.6991118430775
x69 = 59.6902604182061
x70 = -28.2743338823081
x71 = 89.5353906273091
x72 = 29.845130209103
x73 = -59.6902604182061
x74 = -40.8407044966673
x75 = 56.5486677646163
x76 = 34.5575191894877
x77 = 42.4115008234622
x78 = -81.6814089933346
x79 = 87.9645943005142
x80 = -43.9822971502571
x81 = 70.6858347057703
x82 = -14.1371669411541
x83 = 590.619418874881
x84 = -94.2477796076938
x85 = 51.8362787842316
x86 = -75.398223686155
x87 = 4.71238898038469
x88 = 14.1371669411541
x89 = -67.5442420521806
x89 = -67.5442420521806
The graph