Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 15*x^2-4*x-3=0
- Equation 64-x^2=0
-
Equation 16x^2-1=0
-
Equation 0=2-3x
- Express {x} in terms of y where:
- -8*x-2*y=-11
- -20*x-12*y=-17
- 3*x+8*y=-7
- -16*x+7*y=19
- Integral of d{x}:
- cos(-2x)
- Derivative of:
- -√3/2
-
Identical expressions
- cos(- two x)=-√ three /2
- co sinus of e of ( minus 2x) equally minus √3 divide by 2
- co sinus of e of ( minus two x) equally minus √ three divide by 2
- cos-2x=-√3/2
- cos(-2x)=-√3 divide by 2
-
Similar expressions
- cos(-2*x)=-1
- -sin(x)+cos(-2*x+3*pi/2)=0
- (cos(-2*x)+1)*(sin(-x)+1)=0
- cos^-2(x)=1
- cos(-2x)=+√3/2
- cos(2x)=-√3/2
- sin(x)=-(√3/2)
cos(-2x)=-√3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
cos(-2*x) = -------
2
$$\cos{\left(- 2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Detail solution
Given the equation
$$\cos{\left(- 2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Or
$$2 x = \pi n + \frac{5 \pi}{6}$$
$$2 x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{5 \pi}{12}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{12}$$
$$\cos{\left(- 2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Or
$$2 x = \pi n + \frac{5 \pi}{6}$$
$$2 x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{5 \pi}{12}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{12}$$
Rapid solution
[src]
5*pi
x1 = ----
12
$$x_{1} = \frac{5 \pi}{12}$$
7*pi
x2 = ----
12
$$x_{2} = \frac{7 \pi}{12}$$
x2 = 7*pi/12
Sum and product of roots
[src]
sum
5*pi 7*pi ---- + ---- 12 12
$$\frac{5 \pi}{12} + \frac{7 \pi}{12}$$
=
pi
$$\pi$$
product
5*pi 7*pi ----*---- 12 12
$$\frac{5 \pi}{12} \frac{7 \pi}{12}$$
=
2 35*pi ------ 144
$$\frac{35 \pi^{2}}{144}$$
35*pi^2/144
Numerical answer
[src]
x1 = -13.8753675533549
x2 = 39.5317075576716
x3 = -58.3812634792103
x4 = 1336.48587471466
x5 = 1.83259571459405
x6 = -26.9653369433124
x7 = 80.3724120543389
x8 = -1899.35455848283
x9 = 10.7337748997651
x10 = 82.9904059323304
x11 = 60.9992573572018
x12 = 33.248522250492
x13 = -4.97418836818384
x14 = -55.2396708256205
x15 = 11.2573736753634
x16 = -82.9904059323304
x17 = -30.1069295969022
x18 = -74.0892267471593
x19 = -45.8148928648512
x20 = -48.4328867428426
x21 = 42.1497014356631
x22 = 17.540558982543
x23 = 61.5228561328001
x24 = 77.2308194007491
x25 = -48.9564855184409
x26 = -35.8665161284835
x27 = -70.4240353179712
x28 = -17.540558982543
x29 = -61.5228561328001
x30 = -99.2219679758776
x31 = -79.8488132787406
x32 = 89.7971900151083
x33 = 48.4328867428426
x34 = -89.7971900151083
x35 = 35.8665161284835
x36 = -98.6983692002793
x37 = -96.0803753222878
x38 = -52.0980781720307
x39 = 58.3812634792103
x40 = -20.1585528605345
x41 = -32.7249234748937
x42 = 54.7160720500222
x43 = 17.0169602069447
x44 = 20.1585528605345
x45 = 70.4240353179712
x46 = 67.8060414399797
x47 = -39.5317075576716
x48 = 98.6983692002793
x49 = -228.027266773059
x50 = 83.5140047079287
x51 = -77.2308194007491
x52 = 92.4151838930998
x53 = -11.2573736753634
x54 = 64.1408500107916
x55 = 45.8148928648512
x56 = -67.8060414399797
x57 = 99.2219679758776
x58 = 4.45058959258554
x59 = 96.0803753222878
x60 = -1.30899693899575
x61 = -8.11578102177363
x62 = 86.1319985859202
x63 = 76.7072206251508
x64 = 26.4417381677141
x65 = 23.8237442897226
x66 = 32.7249234748937
x67 = -10.7337748997651
x68 = -92.9387826686981
x69 = -86.1319985859202
x70 = -1.83259571459405
x71 = -33.248522250492
x72 = 30.1069295969022
x73 = -83.5140047079287
x74 = 3925.15822127265
x75 = 52.0980781720307
x76 = -26.4417381677141
x77 = -70.9476340935695
x78 = 55.2396708256205
x79 = 74.0892267471593
x80 = -42.1497014356631
x81 = 8.11578102177363
x82 = -89.27359123951
x83 = -64.1408500107916
x84 = -23.8237442897226
x85 = 13.8753675533549
x86 = -45.2912940892529
x87 = -76.7072206251508
x88 = -54.7160720500222
x89 = -57.857664703612
x90 = -92.4151838930998
x91 = 39.0081087820733
x92 = -4.45058959258554
x92 = -4.45058959258554