Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 0*x=0
-
Equation (7x-8)-(2x-5)=17
-
Equation log(x)
-
Equation sin5x=0
- Express {x} in terms of y where:
- -6*x+1*y=14
- 18*x+14*y=-11
- -6*x-2*y=-10
- -10*x+9*y=-6
- Derivative of:
-
sin5x
- Graphing y =:
- sin5x
- Canonical form:
- sin5x
-
Identical expressions
- sin5x= zero
- sinus of 5x equally 0
- sinus of 5x equally zero
- sin5x=O
-
Similar expressions
- sin(5x)=-1/2
- sin(9x)-sin(5x)+sin(4x)=0
- sin(5x)=√2\2
sin5x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(5 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(5 x \right)} = 0$$
This equation is transformed to
$$5 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$5 x = 2 \pi n$$
$$5 x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{\pi}{5}$$
$$\sin{\left(5 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(5 x \right)} = 0$$
This equation is transformed to
$$5 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$5 x = 2 \pi n$$
$$5 x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{\pi}{5}$$
Sum and product of roots
[src]
sum
pi -- 5
$$\frac{\pi}{5}$$
=
pi -- 5
$$\frac{\pi}{5}$$
product
pi 0*-- 5
$$0 \frac{\pi}{5}$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 0.0
x2 = -91.734505484822
x3 = 32.0442450666159
x4 = -11.9380520836412
x5 = 92.3628240155399
x6 = -89.8495498926681
x7 = 70.3716754404114
x8 = -20.1061929829747
x9 = 52.7787565803085
x10 = -27.6460153515902
x11 = -93.6194610769758
x12 = 77.9114978090269
x13 = -71.6283125018473
x14 = 33.9292006587698
x15 = -25.7610597594363
x16 = 82.3097275240526
x17 = -79.7964534011807
x18 = 6.28318530717959
x19 = -69.7433569096934
x20 = 1.88495559215388
x21 = -49.6371639267187
x22 = 67.8584013175395
x23 = 62.2035345410779
x24 = 96.1327351998477
x25 = -43.9822971502571
x26 = -59.6902604182061
x27 = 94.2477796076938
x28 = -65.9734457253857
x29 = -96.1327351998477
x30 = 5.65486677646163
x31 = 89.2212313619501
x32 = -23.8761041672824
x33 = 74.1415866247191
x34 = 42.0973415581032
x35 = 18.2212373908208
x36 = -64.0884901332318
x37 = 50.2654824574367
x38 = 8.16814089933346
x39 = -67.8584013175395
x40 = 11.9380520836412
x41 = 98.0176907920015
x42 = 16.3362817986669
x43 = -47.7522083345649
x44 = 52.1504380495906
x45 = -77.9114978090269
x46 = 21.9911485751286
x47 = -15.707963267949
x48 = 23.8761041672824
x49 = 189.752196276824
x50 = -37.6991118430775
x51 = -99.9026463841554
x52 = 60.318578948924
x53 = -3.76991118430775
x54 = -74.1415866247191
x55 = -10.0530964914873
x56 = -86.0796387083603
x57 = 40.2123859659494
x58 = 64.0884901332318
x59 = -81.6814089933346
x60 = -45.867252742411
x61 = 65.9734457253857
x62 = -13.8230076757951
x63 = 5.02654824574367
x64 = 86.0796387083603
x65 = -42.0973415581032
x66 = -52.7787565803085
x67 = -57.8053048260522
x68 = 43.9822971502571
x69 = 30.159289474462
x70 = -32.0442450666159
x71 = -87.9645943005142
x72 = 54.0353936417444
x73 = 87.9645943005142
x74 = 72.2566310325652
x75 = -35.8141562509236
x76 = -1.88495559215388
x77 = 48.3805268652828
x78 = 26.3893782901543
x79 = 101.159283445591
x80 = 38.3274303737955
x81 = 10.0530964914873
x82 = 84.1946831162065
x83 = -21.9911485751286
x84 = 99.9026463841554
x85 = 28.2743338823081
x86 = 76.026542216873
x87 = -33.9292006587698
x88 = -55.9203492338983
x89 = 11.3097335529233
x90 = -54.0353936417444
x91 = 20.1061929829747
x92 = -5.65486677646163
x93 = 45.867252742411
x94 = -76.026542216873
x95 = -98.0176907920015
x96 = 55.9203492338983
x96 = 55.9203492338983
The graph