Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x-3=4
-
Equation 12-4(x-3)=39-9x
-
Equation x^4=(4x-5)^2
-
Equation (y^4+4*y^2-12)/4=0
- Express {x} in terms of y where:
- -9*x-1*y=6
- -2*x+20*y=-2
- 15*x+9*y=5
- -11*x-19*y=14
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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Identical expressions
- cos(x)=sqrt(two +sqrt(three))/ two
- co sinus of e of (x) equally square root of (2 plus square root of (3)) divide by 2
- co sinus of e of (x) equally square root of (two plus square root of (three)) divide by two
- cos(x)=√(2+√(3))/2
- cosx=sqrt2+sqrt3/2
- cos(x)=sqrt(2+sqrt(3)) divide by 2
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Similar expressions
- sin5x+cos5x=sqrt2cosx
- cos(x/2)=-sqrt2/2
- cos(x)=sqrt(2-sqrt(3))/2
- cosx=sqrt(2+sqrt(3))/2
cos(x)=sqrt(2+sqrt(3))/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___________
/ ___
\/ 2 + \/ 3
cos(x) = --------------
2
$$\cos{\left(x \right)} = \frac{\sqrt{\sqrt{3} + 2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\sqrt{\sqrt{3} + 2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{\sqrt{\sqrt{3} + 2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
, where n - is a integer
Sum and product of roots
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sum
/ ___________\ / ___________\
| / ___ | | / ___ |
|\/ 2 + \/ 3 | |\/ 2 + \/ 3 |
- acos|--------------| + 2*pi + acos|--------------|
\ 2 / \ 2 /
$$\operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)} + \left(- \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
/ / ___________\ \ / ___________\ | | / ___ | | | / ___ | | |\/ 2 + \/ 3 | | |\/ 2 + \/ 3 | |- acos|--------------| + 2*pi|*acos|--------------| \ \ 2 / / \ 2 /
$$\left(- \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
=
/ / ___________\ \ / ___________\ | | / ___ | | | / ___ | | |\/ 2 + \/ 3 | | |\/ 2 + \/ 3 | |- acos|--------------| + 2*pi|*acos|--------------| \ \ 2 / / \ 2 /
$$\left(- \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
(-acos(sqrt(2 + sqrt(3))/2) + 2*pi)*acos(sqrt(2 + sqrt(3))/2)
Rapid solution
[src]
/ ___________\
| / ___ |
|\/ 2 + \/ 3 |
x1 = - acos|--------------| + 2*pi
\ 2 /
$$x_{1} = - \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)} + 2 \pi$$
/ ___________\
| / ___ |
|\/ 2 + \/ 3 |
x2 = acos|--------------|
\ 2 /
$$x_{2} = \operatorname{acos}{\left(\frac{\sqrt{\sqrt{3} + 2}}{2} \right)}$$
x2 = acos(sqrt(sqrt(3) + 2)/2)
Numerical answer
[src]
x1 = 88.2263936883134
x2 = -56.8104671524154
x3 = 93.9859802198946
x4 = 63.093652459595
x5 = 75.1364242983559
x6 = -590.357619487082
x7 = -44.2440965380563
x8 = 50.0036830696375
x9 = -75.1364242983559
x10 = 31.1541271480988
x11 = 6.54498469497874
x12 = 12.8281700021583
x13 = -25.3945406165175
x14 = -18.5877565337396
x15 = 31.6777259236971
x16 = -75.6600230739542
x17 = -0.261799387799149
x18 = -87.7027949127151
x19 = 87.7027949127151
x20 = 100.792764302673
x21 = 62.5700536839967
x22 = -12.8281700021583
x23 = -50.5272818452358
x24 = -56.2868683768171
x25 = -81.4196096055355
x26 = 584.074434179902
x27 = 6.02138591938044
x28 = -31.1541271480988
x29 = 19.1113553093379
x30 = -37.9609112308767
x31 = -716.544924406272
x32 = 50.5272818452358
x33 = 24.8709418409192
x34 = -94.5095789954929
x35 = -63.093652459595
x36 = -31.6777259236971
x37 = 56.2868683768171
x38 = 69.3768377667746
x39 = -62.5700536839967
x40 = 37.9609112308767
x41 = -68.8532389911763
x42 = -50.0036830696375
x43 = 81.4196096055355
x44 = 100.269165527074
x45 = -69.3768377667746
x46 = 44.2440965380563
x47 = -93.9859802198946
x48 = -12.30457122656
x49 = 75.6600230739542
x50 = -19.1113553093379
x51 = 56.8104671524154
x52 = -6.54498469497874
x53 = -24.8709418409192
x54 = -37.4373124552784
x55 = 12.30457122656
x56 = -43.720497762458
x57 = -88.2263936883134
x58 = 18.5877565337396
x59 = -81.9432083811338
x60 = 0.261799387799149
x61 = 37.4373124552784
x62 = -6.02138591938044
x63 = 43.720497762458
x64 = 68.8532389911763
x65 = 25.3945406165175
x66 = 94.5095789954929
x67 = 81.9432083811338
x68 = -100.269165527074
x68 = -100.269165527074