Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x-4)^2-x^2=0
-
Equation 4x+1=-3x+15
-
Equation 1/x^2-3/x-4=0
-
Equation (-x-4)*(3*x+3)=0
- Express {x} in terms of y where:
- -14*x-8*y=20
- -10*x+15*y=10
- 9*x-1*y=-2
- 20*x-14*y=5
- Graphing y =:
- 3cosx-1
-
Identical expressions
- 3cosx- one = zero
- 3 co sinus of e of x minus 1 equally 0
- 3 co sinus of e of x minus one equally zero
- 3cosx-1=O
-
Similar expressions
- 3cosx+1=0
- (x-3)*cos(x)-1=0
3cosx-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$3 \cos{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
We get:
$$3 \cos{\left(x \right)} - 1 + 1 = 1$$
The equation is transformed to
$$\cos{\left(x \right)} = \frac{1}{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
, where n - is a integer
$$3 \cos{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move -1 to right part of the equation
with the change of sign in -1
We get:
$$3 \cos{\left(x \right)} - 1 + 1 = 1$$
Divide both parts of the equation by 3
The equation is transformed to
$$\cos{\left(x \right)} = \frac{1}{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(1/3) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi$$
x2 = acos(1/3)
$$x_{2} = \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Sum and product of roots
[src]
sum
0 + -acos(1/3) + 2*pi + acos(1/3)
$$\operatorname{acos}{\left(\frac{1}{3} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right)\right)$$
=
2*pi
$$2 \pi$$
product
1*(-acos(1/3) + 2*pi)*acos(1/3)
$$1 \left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$
=
(-acos(1/3) + 2*pi)*acos(1/3)
$$\left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$
(-acos(1/3) + 2*pi)*acos(1/3)
Numerical answer
[src]
x1 = 26.3637006460591
x2 = 23.9017818113776
x3 = 36.4681524257367
x4 = 7.51414472452036
x5 = 1.23095941734077
x6 = -30.1849671185572
x7 = 57.7796271819571
x8 = -101.761924332214
x9 = -57.7796271819571
x10 = 86.7336348831734
x11 = 80.4504495759938
x12 = -1.23095941734077
x13 = -61.6008936544551
x14 = -13.7973300316999
x15 = 82.9123684106754
x16 = 95.4787390250346
x17 = 51.4964418747775
x18 = 11.3354111970184
x19 = -82.9123684106754
x20 = 49.0345230400959
x21 = 99.3000054975326
x22 = 67.8840789616347
x23 = 74.1672642688143
x24 = -70.3459977963162
x25 = -325.494676555998
x26 = -38.9300712604183
x27 = -55.3177083472755
x28 = -74.1672642688143
x29 = 70.3459977963162
x30 = -45.2132565675979
x31 = 5.05222588983881
x32 = 93.016820190353
x33 = 89.195553717855
x34 = 17.618596504198
x35 = -32.6468859532387
x36 = -99.3000054975326
x37 = -64.0628124891366
x38 = 55.3177083472755
x39 = -89.195553717855
x40 = 30.1849671185572
x41 = -17.618596504198
x42 = 42.7513377329163
x43 = -26.3637006460591
x44 = -80.4504495759938
x45 = -7.51414472452036
x46 = -42.7513377329163
x47 = 38.9300712604183
x48 = -86.7336348831734
x49 = -51.4964418747775
x50 = -49.0345230400959
x51 = 64.0628124891366
x52 = 45.2132565675979
x53 = 20.0805153388795
x54 = -76.6291831034958
x55 = -20.0805153388795
x56 = -11.3354111970184
x57 = 76.6291831034958
x58 = -95.4787390250346
x59 = -36.4681524257367
x60 = -5.05222588983881
x61 = 13.7973300316999
x62 = -93.016820190353
x63 = -67.8840789616347
x64 = 61.6008936544551
x65 = -23.9017818113776
x66 = 32.6468859532387
x66 = 32.6468859532387
The graph