Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=11
-
Equation log(4/(7-x))/log(x^2)=5
-
Equation 2x-5=7
-
Equation x^4=(x-20)^2
- Express {x} in terms of y where:
- -11*x+6*y=4
- 14*x-13*y=-10
- -14*x-16*y=14
- 16*x-17*y=-9
- Derivative of:
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sin(x)
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1/4
- Integral of d{x}:
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sin(x)
- Limit of the function:
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sin(x)
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1/4
- Canonical form:
- 1/4
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Identical expressions
- sin(x)= one / four
- sinus of (x) equally 1 divide by 4
- sinus of (x) equally one divide by four
- sinx=1/4
- sin(x)=1 divide by 4
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Similar expressions
- cos((pi*(8x-1)/4))=sqtr2/2
- sinx=cosx
- (sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)=0
- sqrt((x-1)/(x+1))*((x-1)/(x+1)-1)*(2/(x+1)+((x-1)/(x+1)-1)/(x-1)+2/(x-1))/(4*(x-1))=0
- 4^(4*x-1)/4^(3*x-1)=1
- (x-1)/(4x-1)=5/2
- sinx=1/4
sin(x)=1/4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{1}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{1}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi - asin(1/4) + asin(1/4)
$$\operatorname{asin}{\left(\frac{1}{4} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{1}{4} \right)}\right)$$
=
pi
$$\pi$$
product
(pi - asin(1/4))*asin(1/4)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{4} \right)}\right) \operatorname{asin}{\left(\frac{1}{4} \right)}$$
=
(pi - asin(1/4))*asin(1/4)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{4} \right)}\right) \operatorname{asin}{\left(\frac{1}{4} \right)}$$
(pi - asin(1/4))*asin(1/4)
Rapid solution
[src]
x1 = pi - asin(1/4)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{4} \right)}$$
x2 = asin(1/4)
$$x_{2} = \operatorname{asin}{\left(\frac{1}{4} \right)}$$
x2 = asin(1/4)
Numerical answer
[src]
x1 = -85.0756819020665
x2 = -72.5093112877073
x3 = 88.2172745556563
x4 = -18.5968756663967
x5 = 72.0039507774232
x6 = 163.615498241811
x7 = -56.2959875094742
x8 = -43.729616895115
x9 = -31.1632462807559
x10 = 81.9340892484767
x11 = -116.491608437964
x12 = 69.3677186341175
x13 = -24.8800609735763
x14 = 59.437580163064
x15 = -100.278284659731
x16 = -81.4287287381925
x17 = -93.9950993525517
x18 = 65.7207654702436
x19 = 0.252680255142079
x20 = 21.7384683199865
x21 = 84.5703213917823
x22 = -91.3588672092461
x23 = -6.03050505203751
x24 = 78.2871360846027
x25 = 6.53586556232167
x26 = 37.9517920982196
x27 = 12.8190508695013
x28 = 144.765942320273
x29 = 50.5181627125788
x30 = 31.66860679104
x31 = 40.5880242415252
x32 = -59.9429406733481
x33 = 9.1720977056273
x34 = -28.5270141374502
x35 = -66.2261259805277
x36 = 2.88891239844771
x37 = -41.0933847518094
x38 = -3.39427290873187
x39 = -22.2438288302706
x40 = -87.7119140453721
x41 = -37.4464315879354
x42 = -9.67745821591146
x43 = 19.1022361766808
x44 = 44.2349774053992
x45 = -62.5791728166538
x46 = 100.783645170015
x47 = -50.0128022022946
x48 = -97.6420525164257
x49 = 25.3854214838604
x50 = 63.0845333269379
x51 = 56.8013480197584
x52 = -47.376570058989
x53 = 90.8535066989619
x54 = -53.6597553661686
x55 = 53.1543948558844
x56 = -34.8101994446298
x57 = 75.6509039412971
x58 = 97.1366920061415
x59 = 34.3048389343456
x60 = -68.8623581238334
x61 = 15.4552830128069
x62 = -12.3136903592171
x63 = -15.960643523091
x64 = 46.8712095487048
x65 = 94.5004598628359
x66 = 28.0216536271661
x67 = -78.7924965948869
x68 = -75.145543431013
x68 = -75.145543431013
The graph