Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x^2+3)/(x^2+1)=2
-
Equation 4x^3-4x=0
-
Equation -x=3,5
-
Equation z^2+z+2=0
- Express {x} in terms of y where:
- 8*x+11*y=-10
- -19*x+9*y=14
- 18*x-3*y=-2
- -6*x-12*y=-17
- Graphing y =:
- |cos(x)|
- Integral of d{x}:
- |cos(x)|
- Derivative of:
- (1/2)
- Sum of series:
-
(1/2)
-
Identical expressions
- |cos(x)|=(one / two)
- module of co sinus of e of (x)| equally (1 divide by 2)
- module of co sinus of e of (x)| equally (one divide by two)
- |cosx|=1/2
- |cos(x)|=(1 divide by 2)
-
Similar expressions
- |cosx|=sinxcisx
- sin(x)^(2)+sqrt(2)*sin(x)*cos(5*x/2-5*pi/8)+1/2=0
- (-3)*121*a*d/2+745*a*d/4+a*d31-31*m*y-3*m*y31/2+1513*m5*x^2*y/25+6*x+9=0
- 3*x+11/9=x-91/27
- 1/4y+7=21-1/2y
- cosx-2|cosx|=y
- |cosx|=(1/2)
|cos(x)|=(1/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
transform
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
Do replacement
$$w = \left|{\cos{\left(x \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\left|{\cos{\left(x \right)}}\right| = w$$
substitute w:
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
transform
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
Do replacement
$$w = \left|{\cos{\left(x \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\left|{\cos{\left(x \right)}}\right| = w$$
substitute w:
Rapid solution
[src]
pi
x1 = --
3
$$x_{1} = \frac{\pi}{3}$$
2*pi
x2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
4*pi
x3 = ----
3
$$x_{3} = \frac{4 \pi}{3}$$
5*pi
x4 = ----
3
$$x_{4} = \frac{5 \pi}{3}$$
x4 = 5*pi/3
Sum and product of roots
[src]
sum
pi 2*pi 4*pi 5*pi -- + ---- + ---- + ---- 3 3 3 3
$$\frac{5 \pi}{3} + \left(\left(\frac{\pi}{3} + \frac{2 \pi}{3}\right) + \frac{4 \pi}{3}\right)$$
=
4*pi
$$4 \pi$$
product
pi 2*pi 4*pi 5*pi --*----*----*---- 3 3 3 3
$$\frac{5 \pi}{3} \frac{4 \pi}{3} \frac{\pi}{3} \frac{2 \pi}{3}$$
=
4 40*pi ------ 81
$$\frac{40 \pi^{4}}{81}$$
40*pi^4/81
Numerical answer
[src]
x1 = -93.2005820564972
x2 = -68.0678408277789
x3 = -79.5870138909414
x4 = 63.8790506229925
x5 = 82.7286065445312
x6 = -85.870199198121
x7 = -4.18879020478639
x8 = 74.3510261349584
x9 = 61.7846555205993
x10 = -35.6047167406843
x11 = 2.0943951023932
x12 = 33.5103216382911
x13 = -76.4454212373516
x14 = -32.4631240870945
x15 = 30.3687289847013
x16 = -63.8790506229925
x17 = 39.7935069454707
x18 = -70.162235930172
x19 = 70.162235930172
x20 = 269.129770657526
x21 = 38.7463093942741
x22 = 76.4454212373516
x23 = -39.7935069454707
x24 = -77.4926187885482
x25 = -96.342174710087
x26 = 85.870199198121
x27 = 98.4365698124802
x28 = -24.0855436775217
x29 = -90.0589894029074
x30 = -41.8879020478639
x31 = -673.348025419412
x32 = 60.7374579694027
x33 = 90.0589894029074
x34 = 275.412955964705
x35 = -2.0943951023932
x36 = 41.8879020478639
x37 = -74.3510261349584
x38 = 26.1799387799149
x39 = 55.5014702134197
x40 = -61.7846555205993
x41 = 68.0678408277789
x42 = -13.6135681655558
x43 = -55.5014702134197
x44 = -30.3687289847013
x45 = 77.4926187885482
x46 = -26.1799387799149
x47 = 8.37758040957278
x48 = 52.3598775598299
x49 = -46.0766922526503
x50 = -33.5103216382911
x51 = 16.7551608191456
x52 = -60.7374579694027
x53 = -99.4837673636768
x54 = -27.2271363311115
x55 = -5.23598775598299
x56 = 96.342174710087
x57 = -11.5191730631626
x58 = -83.7758040957278
x59 = -54.4542726622231
x60 = 3803.42150594604
x61 = 19.8967534727354
x62 = 48.1710873550435
x63 = -49.2182849062401
x64 = -10.471975511966
x65 = 4.18879020478639
x66 = 32.4631240870945
x67 = 11.5191730631626
x68 = 83.7758040957278
x69 = -42.9350995990605
x70 = -71.2094334813686
x71 = -19.8967534727354
x72 = 54.4542726622231
x73 = 99.4837673636768
x74 = 92.1533845053006
x75 = -48.1710873550435
x76 = 46.0766922526503
x77 = 24.0855436775217
x78 = 10.471975511966
x79 = 17.8023583703422
x80 = -17.8023583703422
x81 = -57.5958653158129
x82 = -92.1533845053006
x83 = -52.3598775598299
x84 = -98.4365698124802
x84 = -98.4365698124802