Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin2x=-1
-
Equation sqrt(x-1)=3-x
-
Equation sin3x=1
-
Equation cot(x)=1
- Express {x} in terms of y where:
- 12*x+14*y=-15
- 4*x-7*y=4
- -6*x-12*y=9
- -10*x-18*y=6
- Integral of d{x}:
-
sin3x
- Derivative of:
-
sin3x
- Graphing y =:
- sin3x
-
Identical expressions
- sin3x= one
- sinus of 3x equally 1
- sinus of 3x equally one
-
Similar expressions
- (sin(x)+sin(3x)+sin(5x))/(cos(x)+cos(3x)+cos(5x))=tg(5x)
- sin(x)+sin(2*x)+sin(3*x)=0
- sqrt(3)*cos(x)=sin^3(x)+sqrt(3)*cos^3(x)
- sin(3x)=0
sin3x=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(3 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$3 x = 2 \pi n + \frac{\pi}{2}$$
$$3 x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{6}$$
$$\sin{\left(3 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$3 x = 2 \pi n + \frac{\pi}{2}$$
$$3 x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{6}$$
Sum and product of roots
[src]
sum
pi -- 6
$$\frac{\pi}{6}$$
=
pi -- 6
$$\frac{\pi}{6}$$
product
pi -- 6
$$\frac{\pi}{6}$$
=
pi -- 6
$$\frac{\pi}{6}$$
pi/6
Numerical answer
[src]
x1 = -83.252205476317
x2 = -89.5353907407704
x3 = -56.0250689629876
x4 = -100.007366130834
x5 = -43.458698513903
x6 = 82.2050078076434
x7 = -5.75958652427337
x8 = 10.9955746928717
x9 = -93.7241808501502
x10 = -9.94837684428868
x11 = -47.6474886422567
x12 = 84.2994028383437
x13 = -35.081117920222
x14 = -39.2699083292704
x15 = 75.9218225274375
x16 = -1.57079642588424
x17 = 46.6002908748595
x18 = 96.865773409958
x19 = -68.5914394976747
x20 = -91.6297858015358
x21 = 29.845130315527
x22 = -7.85398150192478
x23 = -14.1371668430111
x24 = -22.5147471967799
x25 = -12.0427717978327
x26 = 63.3554518703442
x27 = -3.66519119284134
x28 = 54.977871797926
x29 = -16.2315619072654
x30 = 0.523598641616331
x31 = 52.8834762893477
x32 = -37.1755131460154
x33 = -58.1194640021532
x34 = 31.9395253654771
x35 = -45.5530935835137
x36 = 40.31710567763
x37 = 48.6946859683928
x38 = 19.3731547552869
x39 = 2.61799372149593
x40 = 80.1106131528868
x41 = 98.9601688300381
x42 = -70.6858348165339
x43 = -41.3643034312689
x44 = 65.4498470876666
x45 = -53.9306741017977
x46 = 94.7713782337162
x47 = -85.3466005833809
x48 = 27.7507352485908
x49 = -79.0634150011636
x50 = -62.308254139164
x51 = 88.4881929539175
x52 = 17.2787592807644
x53 = 71.733032403968
x54 = -81.1578103224548
x55 = 21.4675499464553
x56 = -51.8362786904677
x57 = 78.0162175420896
x58 = -66.4970445282258
x59 = -49.7418836877459
x60 = -37.1755131881972
x61 = -85.3466004035061
x62 = 73.8274274735132
x63 = -60.2138590635982
x64 = 67.5442422190054
x65 = -20.4203520794005
x66 = 42.411500732115
x67 = 8.90117917814493
x68 = 69.6386373203027
x69 = 23.5619450702353
x70 = 25.6563401677065
x71 = -95.8185758682622
x72 = -28.7979326032841
x73 = -24.6091423681141
x74 = 86.3937978904858
x75 = 44.5058957975625
x76 = 50.789081090574
x77 = 34.0339203588006
x78 = -3.66519148254904
x79 = 6.8067839497432
x80 = 61.2610563291673
x81 = -18.3259569854581
x82 = 38.2227106406479
x83 = 90.5825880287766
x84 = -64.4026492298162
x85 = 4.71238881902407
x86 = 92.6769831186997
x87 = -87.4409956689738
x88 = -26.7035377567181
x89 = -66.4970443416682
x89 = -66.4970443416682
The graph