Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation (x^2-4)^2+(x^2-3*x-10)^2=0
-
Equation cos(x)+sin(x)=0
-
Equation 7+x=4
- Express {x} in terms of y where:
- 7*x-2*y=20
- -7*x-7*y=-14
- -15*x+17*y=13
- 20*x+4*y=-7
- Derivative of:
-
cos(x)+sin(x)
- Graphing y =:
- cos(x)+sin(x)
- Canonical form:
- cos(x)+sin(x)
-
Identical expressions
- cos(x)+sin(x)= zero
- co sinus of e of (x) plus sinus of (x) equally 0
- co sinus of e of (x) plus sinus of (x) equally zero
- cosx+sinx=0
- cos(x)+sin(x)=O
-
Similar expressions
- |cosx+sinx|=sqrt(2)sin(2x)
- cosx+sinxcosx+sinx=1
- sqrt(((2-sqrt(3))/2)*(1+cos(x)))+sin(x)=1
- sinx/(1+cosx)+sinx/(1-соsx)=0
- cos(x)-sin(x)=0
- cosx+sinx=0
cos(x)+sin(x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
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
$$\sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
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 = 93.4623814442964
x2 = 21.2057504117311
x3 = 43.1968989868597
x4 = 90.3207887907066
x5 = -10.2101761241668
x6 = -19.6349540849362
x7 = 71.4712328691678
x8 = -44.7676953136546
x9 = -41.6261026600648
x10 = 11.7809724509617
x11 = 18.0641577581413
x12 = 8.63937979737193
x13 = -66.7588438887831
x14 = -60.4756585816035
x15 = 27.4889357189107
x16 = 74.6128255227576
x17 = -29.0597320457056
x18 = 40.0553063332699
x19 = -85.6083998103219
x20 = 33.7721210260903
x21 = -47.9092879672443
x22 = -57.3340659280137
x23 = 84.037603483527
x24 = -54.1924732744239
x25 = -76.1836218495525
x26 = -32.2013246992954
x27 = -73.0420291959627
x28 = 30.6305283725005
x29 = -82.4668071567321
x30 = -38.484510006475
x31 = 96.6039740978861
x32 = -22.776546738526
x33 = -79.3252145031423
x34 = 2.35619449019234
x35 = 68.329640215578
x36 = 65.1880475619882
x37 = -13.3517687777566
x38 = -88.7499924639117
x39 = 80.8960108299372
x40 = -51.0508806208341
x41 = 36.9137136796801
x42 = -69.9004365423729
x43 = -7.06858347057703
x44 = -16.4933614313464
x45 = -3.92699081698724
x46 = 62.0464549083984
x47 = 49.4800842940392
x48 = -98.174770424681
x49 = 46.3384916404494
x50 = 351.072979038659
x51 = -25.9181393921158
x52 = 52.621676947629
x53 = 24.3473430653209
x54 = -107.59954838545
x55 = -0.785398163397448
x56 = 5.49778714378214
x57 = -63.6172512351933
x58 = 99.7455667514759
x59 = 58.9048622548086
x60 = 14.9225651045515
x61 = -91.8915851175014
x62 = 55.7632696012188
x63 = -95.0331777710912
x64 = -35.3429173528852
x65 = 77.7544181763474
x66 = 87.1791961371168
x66 = 87.1791961371168
The graph