Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation 2*x^2+6*x+9=0
-
Equation cos(x/2)=(1/2)
-
Equation (x+2)^2=(1-x)^2
- Express {x} in terms of y where:
- 17*x-18*y=10
- 9*x-4*y=2
- 20*x+6*y=8
- -15*x+17*y=13
- Derivative of:
-
sinx-cosx
- Integral of d{x}:
-
sinx-cosx
- Canonical form:
- sinx-cosx
-
Identical expressions
- sinx-cosx= zero
- sinus of x minus co sinus of e of x equally 0
- sinus of x minus co sinus of e of x equally zero
- sinx-cosx=O
-
Similar expressions
- (tg(x)-1)/(1+tg(x))=sin(x)-cos(x)
- sqrt(3)*sin(x)-cos(x)=2*cos(3x)
- sinx+cosx=0
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
$$\frac{\pi}{4}$$
=
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