Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x=2
-
Equation x^2+7x=18
-
Equation x^2-4x=0
-
Equation (y^4+4*y^2-12)/4=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- -7*x-19*y=-18
- 5*x+12*y=18
- -12*x-8*y=13
- 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)
-
Identical expressions
- cos(x)=√ two *sin(x)
- co sinus of e of (x) equally √2 multiply by sinus of (x)
- co sinus of e of (x) equally √ two multiply by sinus of (x)
- cos(x)=√2sin(x)
- cosx=√2sinx
-
Similar expressions
- sqrt(2)sin((3pi/2)+x)*cos((3pi/2)-x)=cosx
- cos((п/2)+2x)=√(2sinx)
- sin2x+√2sinx=0:
- cosx*cos2x*cos4x=0.125
- (√2sinx+√3)*log(√2*cosx)=0
- sinx*cosx=-cbrt(2)/4
- sin2x+√2*sinx-2cosx-√2=0
- cosx=√2*sinx
cos(x)=√2*sin(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ cos(x) = \/ 2 *sin(x)
$$\cos{\left(x \right)} = \sqrt{2} \sin{\left(x \right)}$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = \sqrt{2} \sin{\left(x \right)}$$
transform:
$$- \frac{\sqrt{2} \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$- \sqrt{2} \tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \sqrt{2} \sin{\left(x \right)}$$
transform:
$$- \frac{\sqrt{2} \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$- \sqrt{2} \tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -sqrt(2)
The equation is transformed to
$$\tan{\left(x \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
$$\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
=
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
$$\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
product
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
$$\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
=
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
$$\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
atan(sqrt(2)/2)
Rapid solution
[src]
/ ___\
|\/ 2 |
x1 = atan|-----|
\ 2 /
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
x1 = atan(sqrt(2)/2)
Numerical answer
[src]
x1 = 19.4650356302091
x2 = 22.6066282837989
x3 = -2.52611294491941
x4 = 35.1729988981581
x5 = 50.8809621661071
x6 = -84.207521938254
x7 = -77.9243366310744
x8 = -90.4907072454336
x9 = -74.7827439774847
x10 = 72.8721107412356
x11 = 76.0137033948254
x12 = -33.9420394808173
x13 = 82.296888702005
x14 = 69.7305180876458
x15 = -87.3491145918438
x16 = 3.75707236226018
x17 = 38.3145915517479
x18 = -55.9331880559459
x19 = 63.4473327804663
x20 = -5.6677055985092
x21 = -24.517261520048
x22 = 47.7393695125173
x23 = 255.084484649444
x24 = 66.5889254340561
x25 = 10.0402576694398
x26 = -27.6588541736378
x27 = 32.0314062445683
x28 = -8.80929825209899
x29 = -46.5084100951765
x30 = 13.1818503230296
x31 = 25.7482209373887
x32 = 94.8632593163642
x33 = 91.7216666627744
x34 = -62.2163733631255
x35 = 85.4384813555948
x36 = -96.7738925526132
x37 = -15.0924835592786
x38 = -18.2340762128684
x39 = -40.2252247879969
x40 = 41.4561842053377
x41 = 44.5977768589275
x42 = 28.8898135909785
x43 = 79.1552960484152
x44 = -68.4995586703051
x45 = -65.3579660167153
x46 = -43.3668174415867
x47 = -49.6500027487663
x48 = -81.0659292846642
x49 = 16.3234429766194
x50 = 60.3057401268765
x51 = -37.0836321344071
x52 = 54.0225548196969
x53 = 98.004851969954
x54 = 6.89866501584997
x55 = 88.5800740091846
x56 = -30.8004468272275
x57 = -99.915485206203
x58 = -52.7915954023561
x59 = -11.9508909056888
x60 = -21.3756688664582
x61 = -59.0747807095357
x62 = 101.146444623544
x63 = -71.6411513238949
x64 = 57.1641474732867
x65 = -93.6322998990234
x66 = 0.615479708670387
x66 = 0.615479708670387