Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x^2+6*x+16=0
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Equation sqrt(x+3)=x-3
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Equation cos(x)=1/4
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Equation 6x-3x+1=8
- Express {x} in terms of y where:
- -6*x+12*y=11
- -13*x-7*y=16
- 5*x+19*y=-3
- 15*x+10*y=-4
- Derivative of:
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cos(x)
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1/4
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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1/4
- Canonical form:
- 1/4
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Identical expressions
- cos(x)= one / four
- co sinus of e of (x) equally 1 divide by 4
- co sinus of e of (x) equally one divide by four
- cosx=1/4
- cos(x)=1 divide by 4
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Similar expressions
- (x-1)/(4x-1)=5/2
- -2cosx=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
- 2sin2x-sinxcosx-3cos2x=0
- cos(pi*(x+1)/4)=√2/2
- cosx/7=-1
- cosx=1/4
cos(x)=1/4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{1}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{1}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-acos(1/4) + 2*pi + acos(1/4)
$$\operatorname{acos}{\left(\frac{1}{4} \right)} + \left(- \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(1/4) + 2*pi)*acos(1/4)
$$\left(- \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{4} \right)}$$
=
(-acos(1/4) + 2*pi)*acos(1/4)
$$\left(- \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{4} \right)}$$
(-acos(1/4) + 2*pi)*acos(1/4)
Rapid solution
[src]
x1 = -acos(1/4) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi$$
x2 = acos(1/4)
$$x_{2} = \operatorname{acos}{\left(\frac{1}{4} \right)}$$
x2 = acos(1/4)
Numerical answer
[src]
x1 = -4.96506923552677
x2 = 17.5314398498859
x3 = 80.3632929216818
x4 = 20.1676719931916
x5 = -95.5658956793466
x6 = 76.7163397578079
x7 = 4.96506923552677
x8 = 95.5658956793466
x9 = -80.3632929216818
x10 = -11.2482545427064
x11 = -189.81367528704
x12 = 45.3004132219099
x13 = 92.929663536041
x14 = -70.4331544506283
x15 = -32.7340426075507
x16 = -55.2305516929635
x17 = -42.6641810786043
x18 = -48.9473663857839
x19 = -36.3809957714247
x20 = 30.0978104642451
x21 = 82.9995250649874
x22 = 64.1499691434487
x23 = -23.8146251570655
x24 = 70.4331544506283
x25 = 57.8667838362691
x26 = 39.0172279147303
x27 = -67.7969223073226
x28 = 67.7969223073226
x29 = 11.2482545427064
x30 = -92.929663536041
x31 = 13.884486686012
x32 = -7.6013013788324
x33 = -76.7163397578079
x34 = 1.31811607165282
x35 = 26.4508573003712
x36 = -17.5314398498859
x37 = -20.1676719931916
x38 = -64.1499691434487
x39 = 7.6013013788324
x40 = 86.6464782288614
x41 = -61.513737000143
x42 = 61.513737000143
x43 = -99.2128488432206
x44 = 51.5835985290895
x45 = 55.2305516929635
x46 = -13.884486686012
x47 = -86.6464782288614
x48 = 42.6641810786043
x49 = -1.31811607165282
x50 = 74.0801076145022
x51 = 48.9473663857839
x52 = -57.8667838362691
x53 = -30.0978104642451
x54 = 36.3809957714247
x55 = -26.4508573003712
x56 = -45.3004132219099
x57 = 89.282710372167
x58 = -51.5835985290895
x59 = 99.2128488432206
x60 = 32.7340426075507
x61 = 23.8146251570655
x62 = -74.0801076145022
x63 = -89.282710372167
x64 = -82.9995250649874
x65 = -39.0172279147303
x66 = -1421.31799549424
x66 = -1421.31799549424
The graph