Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation 1-y^2=2+x
-
Equation 1-7*(4+2*x)=-9-4*x
-
Equation sin(x)=2/3
-
Equation x^3+8=0
- Express {x} in terms of y where:
- -14*x-16*y=14
- -16*x-20*y=6
- -7*x+7*y=-14
- 1*x-4*y=1
- Derivative of:
-
sin(x)
- 2/3
- Integral of d{x}:
-
sin(x)
-
2/3
- Canonical form:
- sin(x)
- 2/3
-
Identical expressions
- sin(x)= two / three
- sinus of (x) equally 2 divide by 3
- sinus of (x) equally two divide by three
- sinx=2/3
- sin(x)=2 divide by 3
-
Similar expressions
- (x-5)/2=2*(3x/7-1/2)/3
- 2sinx+1=0
- sinx-cosx=0
- (2sin^2*x-√3sinx)/(2cosx+1)=0
- 1/(3x+1)-2/(3x-1)-5x/(9x^2-1)=(3x^2)/(1-9x^2)
- sinx=2/3
sin(x)=2/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{2}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{2}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
x1 = pi - asin(2/3)
$$x_{1} = - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
x2 = asin(2/3)
$$x_{2} = \operatorname{asin}{\left(\frac{2}{3} \right)}$$
Sum and product of roots
[src]
sum
0 + pi - asin(2/3) + asin(2/3)
$$\operatorname{asin}{\left(\frac{2}{3} \right)} + \left(0 + \left(- \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi\right)\right)$$
=
pi
$$\pi$$
product
1*(pi - asin(2/3))*asin(2/3)
$$1 \left(- \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi\right) \operatorname{asin}{\left(\frac{2}{3} \right)}$$
=
(pi - asin(2/3))*asin(2/3)
$$\left(- \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi\right) \operatorname{asin}{\left(\frac{2}{3} \right)}$$
(pi - asin(2/3))*asin(2/3)
Numerical answer
[src]
x1 = -30.686198879671
x2 = -161594.831050354
x3 = 94.9775072639208
x4 = 65.2437180691587
x5 = 69.8447660352024
x6 = -74.6684960299281
x7 = -189567.572037918
x8 = 27.5446062260812
x9 = 8.69505030454241
x10 = -99.8012372586464
x11 = 4876.48152602759
x12 = 46.3941621476199
x13 = -29.0040615385351
x14 = 33.8277915332608
x15 = -24.4030135724914
x16 = 13.2960982705861
x17 = 76.127951342382
x18 = -49.5357548012097
x19 = -43.2525694940301
x20 = -16.4376909241759
x21 = -1241.6588258242
x22 = 19.5792835777657
x23 = 88.6943219567412
x24 = 21.2614209189016
x25 = -72.9863586887922
x26 = -2033.34017452882
x27 = 71.5269033763383
x28 = -98.1190999175106
x29 = 8206.56973883277
x30 = 90.376459297877
x31 = -22.7208762313555
x32 = 352.588104858284
x33 = -809.80117696994
x34 = -93.5180519514668
x35 = 82.4111366495616
x36 = -54.1368027672534
x37 = 77.8100886835179
x38 = -5.55345765095262
x39 = -80.9516813371077
x40 = -87.2348666442873
x41 = -41.5704321528943
x42 = 101.2606925711
x43 = 7.01291296340655
x44 = -79.2695439959718
x45 = 52.6773474547995
x46 = -18.1198282653118
x47 = 58.9605327619791
x48 = 57.2783954208432
x49 = 1485.24359749175
x50 = -104.40228522469
x51 = -66.7031733816126
x52 = -35.2872468457147
x53 = 32.1456541921249
x54 = -11.8366429581322
x55 = 14.978235611722
x56 = 63.5615807280228
x57 = 222.323350748648
x58 = -68.3853107227485
x59 = 50.9952101136637
x60 = 84.0932739906975
x61 = -47.8536174600739
x62 = -123.251841146229
x63 = -10.1545056169963
x64 = 915594.458012514
x65 = -55.8189401083893
x66 = 25.8624688849453
x67 = -3.87132030981676
x68 = 0.729727656226966
x69 = -36.9693841868506
x70 = -60.419988074433
x71 = -85.5527293031514
x72 = -91.835914610331
x73 = -62.1021254155689
x74 = 2.41186499736283
x75 = 44.7120248064841
x76 = 40.1109768404403
x77 = 96.6596446050566
x78 = 38.4288394993045
x78 = 38.4288394993045
The graph