Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3*x+50=77
-
Equation x^4=(x-20)^2
-
Equation x+3=-9*x
-
Equation 5-2(x-1)=4-x
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 18*x-12*y=-20
- -19*x+1*y=0
- -7*x-7*y=-14
- Derivative of:
-
cos(x)
- Graphing y =:
-
cos(x)
- Integral of d{x}:
-
cos(x)
-
Identical expressions
- cos(x)=-sqrt(three)/ three
- co sinus of e of (x) equally minus square root of (3) divide by 3
- co sinus of e of (x) equally minus square root of (three) divide by three
- cos(x)=-√(3)/3
- cosx=-sqrt3/3
- cos(x)=-sqrt(3) divide by 3
-
Similar expressions
- 4*cos^4(x)-4*cos^2(x)+3cosxsinx+1=0
- (cos(2*x)*cos(8*x)-cos(10*x))/cos(x+1)=0
- cos(x)=+sqrt(3)/3
- cos(x)=-(sqrt(3)/3)
- cosx=-sqrt(3)/3
cos(x)=-sqrt(3)/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
cos(x) = -------
3
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
, where n - is a integer
Rapid solution
[src]
/ ___ \
|-\/ 3 |
x_1 = - acos|-------| + 2*pi
\ 3 /
$$x_{1} = - \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi$$
/ ___ \
|-\/ 3 |
x_2 = acos|-------|
\ 3 /
$$x_{2} = \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Sum and product of roots
[src]
sum
/ ___ \ / ___ \
|-\/ 3 | |-\/ 3 |
- acos|-------| + 2*pi + acos|-------|
\ 3 / \ 3 /
$$\left(- \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi\right) + \left(\operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}\right)$$
=
2*pi
$$2 \pi$$
product
/ ___ \ / ___ \
|-\/ 3 | |-\/ 3 |
- acos|-------| + 2*pi * acos|-------|
\ 3 / \ 3 /
$$\left(- \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi\right) * \left(\operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}\right)$$
=
/ / ___ \ \ / ___ \ | |-\/ 3 | | |-\/ 3 | |- acos|-------| + 2*pi|*acos|-------| \ \ 3 / / \ 3 /
$$\left(- \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Numerical answer
[src]
x1 = -14.7526466498245
x2 = -16.6632798860735
x3 = -90.1508703359795
x4 = 52.451758492902
x5 = -66.9287623435102
x6 = -2.18627603546528
x7 = 10.3800945788939
x8 = -4.0969092717143
x9 = 21.035831957004
x10 = 29.2296505004326
x11 = 41.7960211147918
x12 = 46.1685731857224
x13 = 58.7349438000816
x14 = 2.18627603546528
x15 = -98.3446888794081
x16 = 65.0181291072611
x17 = -22.9464651932531
x18 = 60.6455770363306
x19 = 22.9464651932531
x20 = -33.6022025713632
x21 = -60.6455770363306
x22 = -96.4340556431591
x23 = 79.4951329578693
x24 = -39.8853878785428
x25 = 96.4340556431591
x26 = 48.0792064219714
x27 = -83.8676850287999
x28 = 98.3446888794081
x29 = 16.6632798860735
x30 = -46.1685731857224
x31 = -54.362391729151
x32 = 8.46946134264487
x33 = -41.7960211147918
x34 = 85.7783182650489
x35 = 77.5844997216203
x36 = 83.8676850287999
x37 = 54.362391729151
x38 = -58.7349438000816
x39 = -79.4951329578693
x40 = 73.2119476506898
x41 = -10.3800945788939
x42 = -29.2296505004326
x43 = -27.3190172641836
x44 = -35.5128358076122
x45 = 92.0615035722285
x46 = 33.6022025713632
x47 = 90.1508703359795
x48 = -85.7783182650489
x49 = 39.8853878785428
x50 = 14.7526466498245
x51 = -48.0792064219714
x52 = -65.0181291072611
x53 = -92.0615035722285
x54 = -71.3013144144407
x55 = -21.035831957004
x56 = 71.3013144144407
x57 = -73.2119476506898
x58 = 27.3190172641836
x59 = 66.9287623435102
x60 = -8.46946134264487
x61 = 4.0969092717143
x62 = 35.5128358076122
x63 = -77.5844997216203
x64 = -52.451758492902
x64 = -52.451758492902
The graph