Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sinx+cosx=0
-
Equation 6*x=0
-
Equation Sqrt(cos^2x-sin^2x)(tg2x-1)=0
- Equation x+((3x-9)/5)=11-((15x-12)/3)
- Express {x} in terms of y where:
- 15*x+15*y=16
- -4*x+18*y=-14
- 8*x+7*y=-13
- -12*x+3*y=-9
- Derivative of:
-
sinx+cosx
- Integral of d{x}:
-
sinx+cosx
- Graphing y =:
-
sinx+cosx
-
Identical expressions
- sinx+cosx= zero
- sinus of x plus co sinus of e of x equally 0
- sinus of x plus co sinus of e of x equally zero
- sinx+cosx=O
-
Similar expressions
- sinx-cosx=0
- sinx+(cosx/2-sinx/2)(cox/2+sinx/2)=0
- 2cos(pi/3-x)=sqrt(3)sin(x)+cos(x^2)
- sin(x)+cos(x)=-1
sinx+cosx=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
$$\left(- \frac{\pi}{4}\right)$$
=
-pi ---- 4
$$- \frac{\pi}{4}$$
product
-pi ---- 4
$$\left(- \frac{\pi}{4}\right)$$
=
-pi ---- 4
$$- \frac{\pi}{4}$$
Numerical answer
[src]
x1 = 93.4623814442964
x2 = 30.6305283725005
x3 = 87.1791961371168
x4 = -85.6083998103219
x5 = 65.1880475619882
x6 = 40.0553063332699
x7 = -7.06858347057703
x8 = -35.3429173528852
x9 = -51.0508806208341
x10 = -22.776546738526
x11 = 33.7721210260903
x12 = -95.0331777710912
x13 = -66.7588438887831
x14 = 43.1968989868597
x15 = 351.072979038659
x16 = -88.7499924639117
x17 = -44.7676953136546
x18 = 8.63937979737193
x19 = 14.9225651045515
x20 = -73.0420291959627
x21 = 68.329640215578
x22 = -19.6349540849362
x23 = -16.4933614313464
x24 = 90.3207887907066
x25 = -13.3517687777566
x26 = -38.484510006475
x27 = 84.037603483527
x28 = -107.59954838545
x29 = -82.4668071567321
x30 = -47.9092879672443
x31 = 71.4712328691678
x32 = -3.92699081698724
x33 = 52.621676947629
x34 = 11.7809724509617
x35 = -29.0597320457056
x36 = -98.174770424681
x37 = 55.7632696012188
x38 = -79.3252145031423
x39 = -63.6172512351933
x40 = -57.3340659280137
x41 = 46.3384916404494
x42 = 99.7455667514759
x43 = 24.3473430653209
x44 = 77.7544181763474
x45 = 18.0641577581413
x46 = 96.6039740978861
x47 = -10.2101761241668
x48 = 74.6128255227576
x49 = 49.4800842940392
x50 = -91.8915851175014
x51 = -60.4756585816035
x52 = -41.6261026600648
x53 = 58.9048622548086
x54 = -54.1924732744239
x55 = 27.4889357189107
x56 = -76.1836218495525
x57 = -69.9004365423729
x58 = -0.785398163397448
x59 = 5.49778714378214
x60 = 36.9137136796801
x61 = 21.2057504117311
x62 = -25.9181393921158
x63 = 62.0464549083984
x64 = 2.35619449019234
x65 = 80.8960108299372
x66 = -32.2013246992954
x66 = -32.2013246992954
The graph