Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2^2-x-1=x^2-5*x-(-1-x^2)
-
Equation cos(x)=(1/2)
-
Equation (x+2)^2=(1-x)^2
-
Equation z^4+1=0
- Express {x} in terms of y where:
- 4*x-15*y=19
- 16*x-17*y=-9
- 7*x-2*y=20
- -7*x-7*y=-14
- Integral of d{x}:
-
sin(5x)
-
-1/2
- Derivative of:
-
sin(5x)
- -1/2
- Limit of the function:
- -1/2
-
Identical expressions
- sin(5x)=- one / two
- sinus of (5x) equally minus 1 divide by 2
- sinus of (5x) equally minus one divide by two
- sin5x=-1/2
- sin(5x)=-1 divide by 2
-
Similar expressions
- (3)/(8y^3+1)-(1)/(2y+1)=(y+3)/(y^2-2y+1)
- 1-e^(-n*(n-1)/(2*4096))=3/4
- (2cosx/2-sqrt2)*(sin5x+2)=0
- sin(5x)=+1/2
- 2sin5x=1
sin(5x)=-1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(5 x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$5 x = 2 \pi n - \frac{\pi}{6}$$
$$5 x = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5} - \frac{\pi}{30}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{7 \pi}{30}$$
$$\sin{\left(5 x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$5 x = 2 \pi n - \frac{\pi}{6}$$
$$5 x = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5} - \frac{\pi}{30}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{7 \pi}{30}$$
Sum and product of roots
[src]
sum
pi 7*pi - -- + ---- 30 30
$$- \frac{\pi}{30} + \frac{7 \pi}{30}$$
=
pi -- 5
$$\frac{\pi}{5}$$
product
-pi 7*pi ----*---- 30 30
$$- \frac{\pi}{30} \frac{7 \pi}{30}$$
=
2 -7*pi ------ 900
$$- \frac{7 \pi^{2}}{900}$$
-7*pi^2/900
Rapid solution
[src]
-pi
x1 = ----
30
$$x_{1} = - \frac{\pi}{30}$$
7*pi
x2 = ----
30
$$x_{2} = \frac{7 \pi}{30}$$
x2 = 7*pi/30
Numerical answer
[src]
x1 = 72.3613507876849
x2 = 76.1312619719927
x3 = 70.2669556852917
x4 = 77.8067780539072
x5 = -99.7979266290358
x6 = 22.0958683302482
x7 = 50.160762702317
x8 = -37.8038315981972
x9 = -13.9277274309148
x10 = -34.0339204138894
x11 = 62.3082542961976
x12 = -88.0693140556339
x13 = 96.2374549549673
x14 = -81.7861287484543
x15 = 50.9985207432743
x16 = -49.1135651511204
x17 = -23.9808239224021
x18 = 18.3259571459405
x19 = -69.6386371545737
x20 = -96.028015444728
x21 = -3.87463093942741
x22 = 8.27286065445312
x23 = -75.9218224617533
x24 = -55.8156294787787
x25 = 45.9719724975306
x26 = -89.7448301375484
x27 = -45.7625329872913
x28 = 6.17846555205993
x29 = 26.2846585350346
x30 = 100.007366139275
x31 = -65.868725970266
x32 = -0.10471975511966
x33 = 63.9837703781121
x34 = -20.629791758573
x35 = -35.709436495804
x36 = 89.9542696477877
x37 = 40.1076662108297
x38 = -25.6563400043166
x39 = 92.8864227911382
x40 = -72.1519112774456
x41 = 9.52949771588904
x42 = 9.94837673636768
x43 = -91.8392252399416
x44 = 86.18435846348
x45 = 23.3525053916841
x46 = 16.2315620435473
x47 = 12.0427718387609
x48 = -27.7507351067098
x49 = -67.9631210726592
x50 = 52.2551578047102
x51 = -91.0014671989843
x52 = -44.0870169053768
x53 = 20.001473227855
x54 = 32.1489648217356
x55 = 74.0368668695995
x56 = 87.8598745453945
x57 = 84.0899633610868
x58 = -64.1932098883514
x59 = -8.0634211442138
x60 = -79.6917336460611
x61 = 56.025068989018
x62 = -41.9926218029836
x63 = -5.55014702134197
x64 = -78.0162175641465
x65 = 82.4144472791722
x66 = -57.9100245811719
x67 = -98.1224105471212
x68 = -10.157816246607
x69 = 28.3790536374278
x70 = -17.6976386152225
x71 = -52.0457182944709
x72 = -85.9749189532407
x73 = -11.8333323285216
x74 = -21.8864288200089
x75 = -59.5855406630864
x76 = -71.733032256967
x77 = -62.9365728269155
x78 = -54.1401133968641
x79 = 33.8244809036501
x80 = 97.9129710368819
x81 = 42.2020613132229
x82 = 94.1430598525741
x83 = 1.98967534727354
x84 = -31.9395253114962
x85 = -47.8569280896845
x86 = -31.5206462910176
x87 = 53.9306738866248
x88 = -15.6032435128293
x89 = 30.0545697193424
x90 = 38.4321501289151
x91 = 60.2138591938044
x92 = 66.0781654805053
x93 = -1.78023583703422
x94 = 43.8775773951374
x94 = 43.8775773951374
The graph