Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3*x^2-8*x-3=0
-
Equation 3*x=5
-
Equation (x+5)^2=0
-
Equation sin(3*x)=-1
- Express {x} in terms of y where:
- -17*x-11*y=16
- -9*x+8*y=-11
- -17*x+14*y=11
- -10*x-20*y=19
- Derivative of:
-
sin(3*x)
-
-1
- Integral of d{x}:
-
sin(3*x)
-
-1
- Limit of the function:
-
sin(3*x)
- Sum of series:
-
-1
-
Identical expressions
- sin(three *x)=- one
- sinus of (3 multiply by x) equally minus 1
- sinus of (three multiply by x) equally minus one
- sin(3x)=-1
- sin3x=-1
-
Similar expressions
- 2*sin(3*x-pi/3)=sqrt(3)
- sin(3*x)=+1
sin(3*x)=-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
$$3 x = 2 \pi n - \frac{\pi}{2}$$
$$3 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{6}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{2}$$
$$\sin{\left(3 x \right)} = -1$$
- 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
$$3 x = 2 \pi n - \frac{\pi}{2}$$
$$3 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{6}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{2}$$
Sum and product of roots
[src]
sum
pi pi - -- + -- 6 2
$$- \frac{\pi}{6} + \frac{\pi}{2}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
-pi pi ----*-- 6 2
$$- \frac{\pi}{6} \frac{\pi}{2}$$
=
2 -pi ----- 12
$$- \frac{\pi^{2}}{12}$$
-pi^2/12
Rapid solution
[src]
-pi
x1 = ----
6
$$x_{1} = - \frac{\pi}{6}$$
pi
x2 = --
2
$$x_{2} = \frac{\pi}{2}$$
x2 = pi/2
Numerical answer
[src]
x1 = -90.5825880642629
x2 = 93.724180981475
x3 = 12.0427717609223
x4 = -57.0722664631985
x5 = -15.1843646196319
x6 = -6.80678413492343
x7 = -71.733032269064
x8 = 24.6091422981059
x9 = -82.2050076419441
x10 = -44.5058957690364
x11 = 76.9690203132814
x12 = -61.2610569029623
x13 = -29.8451300978728
x14 = -75.9218227439853
x15 = 1.57079649551977
x16 = 87.4409956573616
x17 = -40.3171055622449
x18 = -67.544242162189
x19 = 47.6474887440776
x20 = -88.4881929146437
x21 = 62.3082542579151
x22 = -42.4115010822267
x23 = 66.4970443756899
x24 = -19.3731548549645
x25 = 51.8362788945866
x26 = -36.1283154225025
x27 = -27.7507351061628
x28 = -2.61799380552474
x29 = -21.467549936198
x30 = -69.6386372219478
x31 = 97.9129711080124
x32 = 18.3259570974782
x33 = -31.9395254618874
x34 = -59.1666617558465
x35 = 45.5530936447347
x36 = 39.2699077976373
x37 = -38.2227104853721
x38 = -10.9955742377112
x39 = 30.8923277323824
x40 = -42.4115006545154
x41 = 53.9306739466035
x42 = 43.4586985173418
x43 = -73.8274272803725
x44 = -46.6002909322334
x45 = 7.85398173632972
x46 = -34.0339203801376
x47 = 85.3466004238277
x48 = 3.66519159119344
x49 = -86.3937978052948
x50 = 22.5147472195373
x51 = -96.8657738808645
x52 = -65.449847091496
x53 = 91.6297858963776
x54 = -63.3554520074103
x55 = 89.5353907930327
x56 = 16.2315620579746
x57 = -0.523598624935135
x58 = -25.6563400624587
x59 = 9.94837678401611
x60 = -80.1106125819736
x61 = -48.6946862836254
x62 = 74.8746248486494
x63 = -4.71238923573352
x64 = 60.213859223833
x65 = 83.2522049224581
x66 = 26.7035373935834
x67 = 49.7418838263396
x68 = 41.3643033140264
x69 = 28.7979325198376
x70 = 14.1371670949785
x71 = 539.830337690668
x72 = 56.0250689520163
x73 = 70.6858345434363
x74 = -84.2994027162129
x75 = -23.5619450047453
x76 = 20.4203521530692
x77 = -92.676983354992
x78 = 95.8185760523108
x79 = 5.7595866707223
x80 = 68.5914394517514
x81 = 64.4026493112537
x82 = -17.2787597552673
x83 = -13.0899693729028
x84 = -78.0162175465002
x85 = 32.9867232717324
x86 = 72.7802296618859
x87 = 100.007366129944
x87 = 100.007366129944
The graph