Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)-sin(x)=0
-
Equation 5-2x=11-7(x+2)
-
Equation -9(8-9x)=4x+5
-
Equation sin(pi*x)=1
- Express {x} in terms of y where:
- 16*x+7*y=8
- -11*x+4*y=-8
- 17*x-11*y=2
- -14*x+1*y=3
- Canonical form:
- cos(x)-sin(x)
- Derivative of:
-
cos(x)-sin(x)
- Graphing y =:
-
cos(x)-sin(x)
-
Identical expressions
- cos(x)-sin(x)= zero
- co sinus of e of (x) minus sinus of (x) equally 0
- co sinus of e of (x) minus sinus of (x) equally zero
- cosx-sinx=0
- cos(x)-sin(x)=O
-
Similar expressions
- 3^1/2*cosx-sinx=2*cos3x
- cos(x)+sin(x)=0
- sqrt2*(cosx-sinx)-1=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
The equation is transformed to
$$\tan{\left(x \right)} = -1$$
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
Divide both parts of the equation by -1
The equation is transformed to
$$\tan{\left(x \right)} = -1$$
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 = 63.6172512351933
x2 = -65.1880475619882
x3 = 47.9092879672443
x4 = 76.1836218495525
x5 = 57.3340659280137
x6 = 44.7676953136546
x7 = -11.7809724509617
x8 = -8.63937979737193
x9 = -62.0464549083984
x10 = -40.0553063332699
x11 = 3.92699081698724
x12 = 29.0597320457056
x13 = 38.484510006475
x14 = -228.550865548657
x15 = 13.3517687777566
x16 = -30.6305283725005
x17 = 32.2013246992954
x18 = 7.06858347057703
x19 = -43.1968989868597
x20 = -33.7721210260903
x21 = 88.7499924639117
x22 = -49.4800842940392
x23 = -58.9048622548086
x24 = -68.329640215578
x25 = 98.174770424681
x26 = -24.3473430653209
x27 = 35.3429173528852
x28 = 69.9004365423729
x29 = 85.6083998103219
x30 = 1672.11268987317
x31 = -27.4889357189107
x32 = 54.1924732744239
x33 = -84.037603483527
x34 = 19.6349540849362
x35 = 10.2101761241668
x36 = 41.6261026600648
x37 = 79.3252145031423
x38 = -14.9225651045515
x39 = -46.3384916404494
x40 = -5.49778714378214
x41 = -96.6039740978861
x42 = 60.4756585816035
x43 = 51.0508806208341
x44 = 25.9181393921158
x45 = -90.3207887907066
x46 = -74.6128255227576
x47 = -55.7632696012188
x48 = 22.776546738526
x49 = 95.0331777710912
x50 = -93.4623814442964
x51 = -2.35619449019234
x52 = -71.4712328691678
x53 = -52.621676947629
x54 = -99.7455667514759
x55 = 66.7588438887831
x56 = -18.0641577581413
x57 = 0.785398163397448
x58 = 91.8915851175014
x59 = -36.9137136796801
x60 = -80.8960108299372
x61 = 101.316363078271
x62 = -87.1791961371168
x63 = 82.4668071567321
x64 = -21.2057504117311
x65 = 73.0420291959627
x66 = 16.4933614313464
x67 = -77.7544181763474
x67 = -77.7544181763474
The graph