Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation x-x/7=15/7
-
Equation (cos(pi*x)/(x-2))=1/(x-2)
-
Equation sin(2*x)=-1
- Express {x} in terms of y where:
- 10*x+5*y=-17
- 18*x-14*y=-12
- 20*x+5*y=-3
- -2*x-14*y=7
- Integral of d{x}:
- 2sin5x
-
Identical expressions
- 2sin5x= one
- 2 sinus of 5x equally 1
- 2 sinus of 5x equally one
-
Similar expressions
- (2cos(x/2)-√(2))*(sin(5x)+2)=0
- (2cosx/2-sqrt2)*(sin5x+2)=0
- tg(2x)cos(3x)+sin(3x)+(2)^(1/2)*sin(5x)=0
- 2sin(5*x)=-1
2sin5x=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(5 x \right)} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(5 x \right)} = \frac{1}{2}$$
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
$$5 x = 2 \pi n + \frac{\pi}{6}$$
$$5 x = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5} + \frac{\pi}{30}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{\pi}{6}$$
$$2 \sin{\left(5 x \right)} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(5 x \right)} = \frac{1}{2}$$
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
$$5 x = 2 \pi n + \frac{\pi}{6}$$
$$5 x = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5} + \frac{\pi}{30}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{\pi}{6}$$
Sum and product of roots
[src]
sum
pi pi -- + -- 30 6
$$\frac{\pi}{30} + \frac{\pi}{6}$$
=
pi -- 5
$$\frac{\pi}{5}$$
product
pi pi --*-- 30 6
$$\frac{\pi}{30} \frac{\pi}{6}$$
=
2 pi --- 180
$$\frac{\pi^{2}}{180}$$
pi^2/180
Rapid solution
[src]
pi
x1 = --
30
$$x_{1} = \frac{\pi}{30}$$
pi
x2 = --
6
$$x_{2} = \frac{\pi}{6}$$
x2 = pi/6
Numerical answer
[src]
x1 = -32.1489648217356
x2 = -23.7713844121628
x3 = 94.3524993628135
x4 = 0.10471975511966
x5 = 1.36135681655558
x6 = 11.8333323285216
x7 = 98.1224105471212
x8 = -16.2315620435473
x9 = -39.6887871903511
x10 = 84.2994028713261
x11 = 12.6710903694788
x12 = -42.2020613132229
x13 = 88.0693140556339
x14 = 55.8156294787787
x15 = -69.8480766648131
x16 = 72.1519112774456
x17 = 96.028015444728
x18 = -59.7949801733257
x19 = 22.7241868609662
x20 = -58.5383431118898
x21 = -57.7005850709325
x22 = 83.4616448303688
x23 = -93.7241808320955
x24 = 48.2758071101632
x25 = 16.4410015537866
x26 = 44.0870169053768
x27 = -67.7536815624199
x28 = 41.9926218029836
x29 = -71.104713726249
x30 = -91.6297857297023
x31 = 65.868725970266
x32 = 50.3702022125564
x33 = -47.6474885794452
x34 = 54.1401133968641
x35 = -86.18435846348
x36 = -74.0368668695995
x37 = -15.8126830230686
x38 = -1.98967534727354
x39 = -5.75958653158129
x40 = -27.1224165759919
x41 = 67.9631210726592
x42 = -20.001473227855
x43 = -87.8598745453945
x44 = -30.0545697193424
x45 = -100.007366139275
x46 = -56.025068989018
x47 = 20.2109127380943
x48 = 82.2050077689329
x49 = 23.9808239224021
x50 = 10.157816246607
x51 = 38.2227106186758
x52 = 31.9395253114962
x53 = -22.0958683302482
x54 = 34.0339204138894
x55 = 64.1932098883514
x56 = -97.9129710368819
x57 = 92.2581042604203
x58 = -81.576689238215
x59 = -12.0427718387609
x60 = -53.9306738866248
x61 = 21.8864288200089
x62 = -89.9542696477877
x63 = -25.865779514556
x64 = 60.4232987040437
x65 = -63.9837703781121
x66 = -98.7507290778392
x67 = 70.8952742160097
x68 = 78.0162175641465
x69 = -3.66519142918809
x70 = -13.7182879206754
x71 = 99.7979266290358
x72 = 52.0457182944709
x73 = -45.9719724975306
x74 = 40.317105721069
x75 = -33.8244809036501
x76 = 30.2640092295817
x77 = -9.94837673636768
x78 = -76.1312619719927
x79 = -90.3731486682664
x80 = 18.1165176357011
x81 = 4.29350995990605
x82 = -49.7418836818384
x83 = 6.38790506229925
x84 = 8.0634211442138
x85 = 28.1696141271885
x86 = 74.2463063798388
x87 = 43.2492588644195
x88 = -79.9011731563004
x89 = -43.8775773951374
x90 = 62.0988147859582
x91 = -77.8067780539072
x92 = -35.9188760060433
x93 = 85.9749189532407
x94 = -37.5943920879579
x95 = 75.9218224617533
x96 = -66.0781654805053
x96 = -66.0781654805053