Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=-3
-
Equation 1/x^2+2/x-3=0
-
Equation 4=7-6(5x-1)
-
Equation cos(x)=-sin(x)
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- -3*x+19*y=16
- Derivative of:
-
cos(x)
-
-sin(x)
- Graphing y =:
-
cos(x)
-
-sin(x)
- Integral of d{x}:
-
cos(x)
- Limit of the function:
-
-sin(x)
-
Identical expressions
- cos(x)=-sin(x)
- co sinus of e of (x) equally minus sinus of (x)
- cosx=-sinx
-
Similar expressions
- cos(x)=+sin(x)
- cos(x/3)=-1/2
- sin2x+1=cosx+2sinx
- √sinxcosx=cosx
- cosx=-sinx
cos(x)=-sin(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \sin{\left(x \right)}$$
transform:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$\tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \sin{\left(x \right)}$$
transform:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$\tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-pi ---- 4
$$- \frac{\pi}{4}$$
=
-pi ---- 4
$$- \frac{\pi}{4}$$
product
-pi ---- 4
$$- \frac{\pi}{4}$$
=
-pi ---- 4
$$- \frac{\pi}{4}$$
-pi/4
Numerical answer
[src]
x1 = 27.4889357189107
x2 = 90.3207887907066
x3 = -66.7588438887831
x4 = -29.0597320457056
x5 = -60.4756585816035
x6 = -13.3517687777566
x7 = -63.6172512351933
x8 = 14.9225651045515
x9 = -79.3252145031423
x10 = 68.329640215578
x11 = -35.3429173528852
x12 = -44.7676953136546
x13 = -98.174770424681
x14 = 49.4800842940392
x15 = 33.7721210260903
x16 = 24.3473430653209
x17 = -107.59954838545
x18 = -85.6083998103219
x19 = 36.9137136796801
x20 = -54.1924732744239
x21 = 5.49778714378214
x22 = 43.1968989868597
x23 = 58.9048622548086
x24 = 11.7809724509617
x25 = 8.63937979737193
x26 = -51.0508806208341
x27 = 351.072979038659
x28 = 30.6305283725005
x29 = 40.0553063332699
x30 = 99.7455667514759
x31 = 80.8960108299372
x32 = -69.9004365423729
x33 = -95.0331777710912
x34 = -47.9092879672443
x35 = -7.06858347057703
x36 = -91.8915851175014
x37 = -41.6261026600648
x38 = 87.1791961371168
x39 = 84.037603483527
x40 = -25.9181393921158
x41 = -32.2013246992954
x42 = 74.6128255227576
x43 = 96.6039740978861
x44 = 93.4623814442964
x45 = 2.35619449019234
x46 = -73.0420291959627
x47 = 71.4712328691678
x48 = 65.1880475619882
x49 = -82.4668071567321
x50 = -10.2101761241668
x51 = -16.4933614313464
x52 = 77.7544181763474
x53 = 18.0641577581413
x54 = 55.7632696012188
x55 = -0.785398163397448
x56 = 46.3384916404494
x57 = 21.2057504117311
x58 = 62.0464549083984
x59 = -3.92699081698724
x60 = -22.776546738526
x61 = -88.7499924639117
x62 = -38.484510006475
x63 = -76.1836218495525
x64 = -19.6349540849362
x65 = 52.621676947629
x66 = -57.3340659280137
x66 = -57.3340659280137
The graph