Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)=sin(x)
-
Equation cos(x)=sqrt(2)/2
-
Equation sin(x)+1/2=0
-
Equation (7x+9)-(11x-7)=8
- Express {x} in terms of y where:
- 10*x+9*y=-4
- -12*x+3*y=-9
- 9*x-18*y=6
- -1*x+19*y=-10
- Derivative of:
-
cos(x)
-
sin(x)
- Integral of d{x}:
-
cos(x)
-
sin(x)
- Graphing y =:
-
cos(x)
- Canonical form:
- sin(x)
-
Identical expressions
- cos(x)=sin(x)
- co sinus of e of (x) equally sinus of (x)
- cosx=sinx
-
Similar expressions
- 5cosx+sin4x−10x=x3+5
- sinx=1/2
- sinx/1+cosx=1-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
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
$$\cos{\left(x \right)} = \sin{\left(x \right)}$$
transform:
$$- \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$- \tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
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 = 1672.11268987317
x2 = -40.0553063332699
x3 = 95.0331777710912
x4 = 32.2013246992954
x5 = -49.4800842940392
x6 = 69.9004365423729
x7 = 38.484510006475
x8 = 85.6083998103219
x9 = -93.4623814442964
x10 = -27.4889357189107
x11 = 76.1836218495525
x12 = -228.550865548657
x13 = -14.9225651045515
x14 = 66.7588438887831
x15 = -18.0641577581413
x16 = 101.316363078271
x17 = -8.63937979737193
x18 = -46.3384916404494
x19 = 51.0508806208341
x20 = -71.4712328691678
x21 = -87.1791961371168
x22 = 3.92699081698724
x23 = -21.2057504117311
x24 = 73.0420291959627
x25 = 54.1924732744239
x26 = 16.4933614313464
x27 = 7.06858347057703
x28 = -65.1880475619882
x29 = 60.4756585816035
x30 = 44.7676953136546
x31 = -99.7455667514759
x32 = 13.3517687777566
x33 = 10.2101761241668
x34 = 29.0597320457056
x35 = -68.329640215578
x36 = -2.35619449019234
x37 = 41.6261026600648
x38 = 91.8915851175014
x39 = -24.3473430653209
x40 = -5.49778714378214
x41 = -96.6039740978861
x42 = 82.4668071567321
x43 = 0.785398163397448
x44 = 25.9181393921158
x45 = 98.174770424681
x46 = 57.3340659280137
x47 = -58.9048622548086
x48 = -52.621676947629
x49 = 35.3429173528852
x50 = -84.037603483527
x51 = -30.6305283725005
x52 = -36.9137136796801
x53 = -90.3207887907066
x54 = 22.776546738526
x55 = -77.7544181763474
x56 = -80.8960108299372
x57 = 88.7499924639117
x58 = -33.7721210260903
x59 = -55.7632696012188
x60 = -62.0464549083984
x61 = -43.1968989868597
x62 = 19.6349540849362
x63 = 79.3252145031423
x64 = 47.9092879672443
x65 = -74.6128255227576
x66 = 63.6172512351933
x67 = -11.7809724509617
x67 = -11.7809724509617
The graph