Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
-
Equation x/4+13=x+1
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
- Derivative of:
-
cos(x+2)
- Integral of d{x}:
-
cos(x+2)
- Graphing y =:
- cos(x+2)
-
Identical expressions
- cos(x+ two)
- co sinus of e of (x plus 2)
- co sinus of e of (x plus two)
- cosx+2
-
Similar expressions
- cos(x-2)
- cos(x+(2*pi)/3)=0
- cosx+2cos(2x-р/3)=√3sin2x-1
- sinxcosx+2sin2x=cos2x
- (4/9)^cosx+2*(2/3)^cosx-3=0
- 2*(3^(1/2))*cos(x)+2*sin(2*x)=3+2*(3^(1/2))*sin(x)
cos(x+2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x + 2 \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x + 2 \right)} = 0$$
This equation is transformed to
$$x + 2 = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + 2 = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + 2 = \pi n + \frac{\pi}{2}$$
$$x + 2 = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$2$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n - 2 + \frac{\pi}{2}$$
$$x = \pi n - 2 - \frac{\pi}{2}$$
$$\cos{\left(x + 2 \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(x + 2 \right)} = 0$$
This equation is transformed to
$$x + 2 = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + 2 = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + 2 = \pi n + \frac{\pi}{2}$$
$$x + 2 = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$2$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n - 2 + \frac{\pi}{2}$$
$$x = \pi n - 2 - \frac{\pi}{2}$$
Rapid solution
[src]
pi
x1 = -2 + --
2
$$x_{1} = -2 + \frac{\pi}{2}$$
3*pi
x2 = -2 + ----
2
$$x_{2} = -2 + \frac{3 \pi}{2}$$
x2 = -2 + 3*pi/2
Sum and product of roots
[src]
sum
pi 3*pi
-2 + -- + -2 + ----
2 2
$$\left(-2 + \frac{\pi}{2}\right) + \left(-2 + \frac{3 \pi}{2}\right)$$
=
-4 + 2*pi
$$-4 + 2 \pi$$
product
/ pi\ / 3*pi\ |-2 + --|*|-2 + ----| \ 2 / \ 2 /
$$\left(-2 + \frac{\pi}{2}\right) \left(-2 + \frac{3 \pi}{2}\right)$$
=
(4 - pi)*(4 - 3*pi)
-------------------
4
$$\frac{\left(4 - 3 \pi\right) \left(4 - \pi\right)}{4}$$
(4 - pi)*(4 - 3*pi)/4
Numerical answer
[src]
x1 = 49.8362787842316
x2 = -47.553093477052
x3 = 65.5442420521806
x4 = 100.101761241668
x5 = -50.6946861306418
x6 = -72.6858347057703
x7 = -97.8185759344887
x8 = 62.4026493985908
x9 = 68.6858347057703
x10 = 96.9601685880785
x11 = -2268.65909956504
x12 = -0.429203673205103
x13 = 56.1194640914112
x14 = 40.4115008234622
x15 = -22.4203522483337
x16 = -53.8362787842316
x17 = -44.4115008234622
x18 = 15.2787595947439
x19 = 27.845130209103
x20 = -85.2522053201295
x21 = 71.8274273593601
x22 = -38.1283155162826
x23 = 90.6769832808989
x24 = -3.5707963267949
x25 = 8.99557428756428
x26 = 21.5619449019235
x27 = -88.3937979737193
x28 = -78.9690200129499
x29 = 37.2699081698724
x30 = -75.8274273593601
x31 = 12.1371669411541
x32 = -16.1371669411541
x33 = 43.553093477052
x34 = 81.2522053201295
x35 = 78.1106126665397
x36 = 74.9690200129499
x37 = 93.8185759344887
x38 = -31.845130209103
x39 = -6.71238898038469
x40 = 46.6946861306418
x41 = 34.1283155162826
x42 = 84.3937979737193
x43 = -63.261056745001
x44 = 30.9867228626928
x45 = -100.960168588078
x46 = 52.9778714378214
x47 = -19.2787595947439
x48 = 2.71238898038469
x49 = -9.85398163397448
x50 = -25.5619449019235
x51 = -41.2699081698724
x52 = -69.5442420521806
x53 = -170.075206967054
x54 = -28.7035375555132
x55 = -12.9955742875643
x56 = -60.1194640914112
x57 = -56.9778714378214
x58 = 5.85398163397448
x59 = -34.9867228626928
x60 = -66.4026493985908
x61 = 59.261056745001
x62 = 24.7035375555132
x63 = 87.5353906273091
x64 = -91.5353906273091
x65 = -82.1106126665397
x66 = -389.986692718339
x67 = 18.4203522483337
x68 = -94.6769832808989
x68 = -94.6769832808989