Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x^2-1)/(x+2)=4x
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation cos(x)=3/4
-
Equation cos(x)=(1/2)
- Express {x} in terms of y where:
- -13*x+7*y=11
- -8*x-15*y=15
- 4*x+18*y=-14
- -15*x-17*y=13
- Derivative of:
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cos(x)
- Graphing y =:
-
cos(x)
- Integral of d{x}:
-
cos(x)
-
Identical expressions
- cos(x)
- co sinus of e of (x)
- cosx
-
Similar expressions
- cosx
cos(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x \right)} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x = \pi n + \frac{\pi}{2}$$
$$x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
$$\cos{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(x \right)} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x = \pi n + \frac{\pi}{2}$$
$$x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 2 2
$$\frac{\pi}{2} + \frac{3 \pi}{2}$$
=
2*pi
$$2 \pi$$
product
pi 3*pi --*---- 2 2
$$\frac{\pi}{2} \frac{3 \pi}{2}$$
=
2 3*pi ----- 4
$$\frac{3 \pi^{2}}{4}$$
3*pi^2/4
Rapid solution
[src]
pi
x1 = --
2
$$x_{1} = \frac{\pi}{2}$$
3*pi
x2 = ----
2
$$x_{2} = \frac{3 \pi}{2}$$
x2 = 3*pi/2
Numerical answer
[src]
x1 = -76.9690200129499
x2 = -17.2787595947439
x3 = 95.8185759344887
x4 = -70.6858347057703
x5 = 86.3937979737193
x6 = -4.71238898038469
x7 = 76.9690200129499
x8 = -36.1283155162826
x9 = -168.075206967054
x10 = 42.4115008234622
x11 = -23.5619449019235
x12 = -61.261056745001
x13 = -92.6769832808989
x14 = -39.2699081698724
x15 = -89.5353906273091
x16 = 64.4026493985908
x17 = 1.5707963267949
x18 = 20.4203522483337
x19 = -58.1194640914112
x20 = -32.9867228626928
x21 = -83.2522053201295
x22 = 92.6769832808989
x23 = 26.7035375555132
x24 = -20.4203522483337
x25 = -42.4115008234622
x26 = 61.261056745001
x27 = -51.8362787842316
x28 = -29.845130209103
x29 = 70.6858347057703
x30 = -10.9955742875643
x31 = -14.1371669411541
x32 = 98.9601685880785
x33 = 32.9867228626928
x34 = 67.5442420521806
x35 = -26.7035375555132
x36 = -80.1106126665397
x37 = 83.2522053201295
x38 = -64.4026493985908
x39 = -73.8274273593601
x40 = 45.553093477052
x41 = -48.6946861306418
x42 = -1.5707963267949
x43 = 23.5619449019235
x44 = 51.8362787842316
x45 = -95.8185759344887
x46 = 10.9955742875643
x47 = 36.1283155162826
x48 = 48.6946861306418
x49 = 80.1106126665397
x50 = 17.2787595947439
x51 = -387.986692718339
x52 = 58.1194640914112
x53 = 4.71238898038469
x54 = 39.2699081698724
x55 = -54.9778714378214
x56 = -86.3937979737193
x57 = -7.85398163397448
x58 = 7.85398163397448
x59 = 14.1371669411541
x60 = -2266.65909956504
x61 = -98.9601685880785
x62 = 89.5353906273091
x63 = 73.8274273593601
x64 = 29.845130209103
x65 = -45.553093477052
x66 = -67.5442420521806
x67 = 54.9778714378214
x67 = 54.9778714378214
The graph