Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation |x^2-1|-|x-3|=7
-
Equation 2x=18-x
-
Equation cos(x)+sin(x)=0
-
Equation 5-2*x=11-7*(x+2)
- Express {x} in terms of y where:
- -6*x-17*y=14
- 9*x+18*y=3
- 13*x-15*y=-6
- 4*x-18*y=-14
- Derivative of:
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sin(t)
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1/3
- Limit of the function:
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sin(t)
- 1/3
- Integral of d{x}:
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sin(t)
- Sum of series:
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1/3
-
Identical expressions
- sin(t)= one / three
- sinus of (t) equally 1 divide by 3
- sinus of (t) equally one divide by three
- sint=1/3
- sin(t)=1 divide by 3
-
Similar expressions
- sint=-1/2
- sint-2sintcost-cost+1=0
- log(1)/9*(x-8)*2+log(1)/3*(2-x)=log(1)/327
- 1/(3x+1)-2/(3x-1)-5x/(9x^2-1)=(3x^2)/(1-9x^2)
- cos(pi*(x-1)/3)=1/2
sin(t)=1/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(t \right)} = \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
Or
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(t \right)} = \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
Or
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
t1 = pi - asin(1/3)
$$t_{1} = \pi - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
t2 = asin(1/3)
$$t_{2} = \operatorname{asin}{\left(\frac{1}{3} \right)}$$
t2 = asin(1/3)
Sum and product of roots
[src]
sum
pi - asin(1/3) + asin(1/3)
$$\operatorname{asin}{\left(\frac{1}{3} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{1}{3} \right)}\right)$$
=
pi
$$\pi$$
product
(pi - asin(1/3))*asin(1/3)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{3} \right)}\right) \operatorname{asin}{\left(\frac{1}{3} \right)}$$
=
(pi - asin(1/3))*asin(1/3)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{3} \right)}\right) \operatorname{asin}{\left(\frac{1}{3} \right)}$$
(pi - asin(1/3))*asin(1/3)
Numerical answer
[src]
t1 = -85.1628385563785
t2 = -43.642460240803
t3 = -47.463726713301
t4 = -34.8973560989418
t5 = -112585.595763607
t6 = 78.1999794302907
t7 = -75.0583867767009
t8 = -60.0300973276602
t9 = 94.5876165171479
t10 = 25.4725781381725
t11 = -53.7469120204806
t12 = 50.6053193668908
t13 = -22.3309854845827
t14 = 172.447759037984
t15 = -24.7929043192642
t16 = 46.7840528943928
t17 = -12.2265337049051
t18 = -72.5964679420194
t19 = -93.9079426982397
t20 = -116.578765092276
t21 = -18.5097190120846
t22 = 88.3044312099683
t23 = 34.2176822800336
t24 = 2.80175574413567
t25 = -66.3132826348398
t26 = 84.4831647374703
t27 = 0.339836909454122
t28 = 71.9167941231111
t29 = 40.5008675872132
t30 = 65.6336088159315
t31 = 12.9062075238133
t32 = -49.9256455479826
t33 = 75.7380605956092
t34 = 19.1893928309929
t35 = -56.2088308551622
t36 = 56.8885046740704
t37 = 82.0212459027887
t38 = 6.62302221663371
t39 = -91.4460238635581
t40 = -28.6141707917623
t41 = 9.08494105131526
t42 = 90.7663500446499
t43 = 63.17168998125
t44 = -100.191128005419
t45 = 44.3221340597112
t46 = 31.7557634453521
t47 = -37.3592749336234
t48 = 69.4548752884296
t49 = -62.4920161623417
t50 = 38.0389487525316
t51 = 97.0495353518295
t52 = -97.7292091707377
t53 = -31.0760896264438
t54 = -16.0478001774031
t55 = 15.3681263584948
t56 = 53.0672382015724
t57 = -5.94334839772546
t58 = 27.934496972854
t59 = 21.6513116656744
t60 = 951.562737128253
t61 = -3.48142956304392
t62 = 100.870801824328
t63 = 59.350423508752
t64 = -87.6247573910601
t65 = -68.7752014695213
t66 = -41.1805414061214
t67 = -78.879653249199
t68 = -9.7646148702235
t69 = -81.3415720838805
t69 = -81.3415720838805