Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+10)^2=(5-x)^2
-
Equation sin(x)=-1/4
-
Equation 3x-3=7x-3(2x-5)
-
Equation k^2-2*k+1=0
- Express {x} in terms of y where:
- 9*x-18*y=6
- -10*x+18*y=6
- 17*x-19*y=1
- -1*x+19*y=-10
- Derivative of:
-
sin(x)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
- Limit of the function:
- -1/4
-
Identical expressions
- sin(x)=- one / four
- sinus of (x) equally minus 1 divide by 4
- sinus of (x) equally minus one divide by four
- sinx=-1/4
- sin(x)=-1 divide by 4
-
Similar expressions
- 2sin^2x+cos^2x-3sinx-5=0
- (x-1)/(4x-1)=5/2
- 2sin^2x+3sinxcosx-5cos^2x=0
- cosx/1+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
- (x-1)/4-(x+5)/10=12
- sinx=1/3
- sin(x)=+1/4
- cos((pi*(8x-1)/4))=sqtr2/2
- 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
Rapid solution
[src]
x1 = pi + asin(1/4)
$$x_{1} = \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
x2 = -asin(1/4)
$$x_{2} = - \operatorname{asin}{\left(\frac{1}{4} \right)}$$
x2 = -asin(1/4)
Sum and product of roots
[src]
sum
pi + asin(1/4) - asin(1/4)
$$- \operatorname{asin}{\left(\frac{1}{4} \right)} + \left(\operatorname{asin}{\left(\frac{1}{4} \right)} + \pi\right)$$
=
pi
$$\pi$$
product
(pi + asin(1/4))*(-asin(1/4))
$$\left(\operatorname{asin}{\left(\frac{1}{4} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{4} \right)}\right)$$
=
-(pi + asin(1/4))*asin(1/4)
$$- \left(\operatorname{asin}{\left(\frac{1}{4} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{4} \right)}$$
-(pi + asin(1/4))*asin(1/4)
Numerical answer
[src]
x1 = 50.0128022022946
x2 = -63.0845333269379
x3 = -94.5004598628359
x4 = -88.2172745556563
x5 = 81.4287287381925
x6 = -53.1543948558844
x7 = -56.8013480197584
x8 = -270.429648463864
x9 = -100.783645170015
x10 = -65.7207654702436
x11 = -50.5181627125788
x12 = -44.2349774053992
x13 = 41.0933847518094
x14 = 59.9429406733481
x15 = 97.6420525164257
x16 = -0.252680255142079
x17 = 31.1632462807559
x18 = -31.66860679104
x19 = 28.5270141374502
x20 = -6.53586556232167
x21 = -19.1022361766808
x22 = 93.9950993525517
x23 = 72.5093112877073
x24 = -28.0216536271661
x25 = 78.7924965948869
x26 = 85.0756819020665
x27 = -78.2871360846027
x28 = 43.729616895115
x29 = -25.3854214838604
x30 = 87.7119140453721
x31 = -37.9517920982196
x32 = -90.8535066989619
x33 = 100.278284659731
x34 = 3.39427290873187
x35 = 47.376570058989
x36 = -81.9340892484767
x37 = -34.3048389343456
x38 = 24.8800609735763
x39 = 68.8623581238334
x40 = -12.8190508695013
x41 = 66.2261259805277
x42 = -75.6509039412971
x43 = 18.5968756663967
x44 = 9.67745821591146
x45 = 22.2438288302706
x46 = 190160.350641535
x47 = 34.8101994446298
x48 = -2.88891239844771
x49 = 12.3136903592171
x50 = -72.0039507774232
x51 = -69.3677186341175
x52 = 6.03050505203751
x53 = -46.8712095487048
x54 = -15.4552830128069
x55 = 37.4464315879354
x56 = -59.437580163064
x57 = -40.5880242415252
x58 = -21.7384683199865
x59 = 15.960643523091
x60 = -97.1366920061415
x61 = 53.6597553661686
x62 = 75.145543431013
x63 = -9.1720977056273
x64 = -84.5703213917823
x65 = 56.2959875094742
x66 = 91.3588672092461
x67 = 62.5791728166538
x67 = 62.5791728166538
The graph