Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 1-5*x=-6*x+8
-
Equation 3-3*6+2=x
-
Equation cos(x/2)=-(1/2)
-
Equation x^2-3*x+3=0
- Express {x} in terms of y where:
- 10*x-2*y=0
- 2*x+1*y=-8
- 2*x+2*y=-6
- 12*x-13*y=-14
- Graphing y =:
- sin(x-pi/4)
- Integral of d{x}:
- sin(x-pi/4)
-
Identical expressions
- sin(x-pi/ four)= zero
- sinus of (x minus Pi divide by 4) equally 0
- sinus of (x minus Pi divide by four) equally zero
- sinx-pi/4=0
- sin(x-pi/4)=O
- sin(x-pi divide by 4)=0
-
Similar expressions
- sin(x+pi/4)=0
- 2*sin(x-(pi/4))=1
sin(x-pi/4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x - \frac{\pi}{4} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(x - \frac{\pi}{4} \right)} = 0$$
The equation is transformed to
$$\cos{\left(x + \frac{\pi}{4} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{4} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
$$\sin{\left(x - \frac{\pi}{4} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(x - \frac{\pi}{4} \right)} = 0$$
Divide both parts of the equation by -1
The equation is transformed to
$$\cos{\left(x + \frac{\pi}{4} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{4} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{5 \pi}{4}$$
=
3*pi ---- 2
$$\frac{3 \pi}{2}$$
product
pi 5*pi --*---- 4 4
$$\frac{\pi}{4} \frac{5 \pi}{4}$$
=
2 5*pi ----- 16
$$\frac{5 \pi^{2}}{16}$$
5*pi^2/16
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
5*pi
x2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*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 = -1535.45340944201
x31 = 44.7676953136546
x32 = -99.7455667514759
x33 = 13.3517687777566
x34 = 10.2101761241668
x35 = 29.0597320457056
x36 = -68.329640215578
x37 = -2.35619449019234
x38 = 41.6261026600648
x39 = 91.8915851175014
x40 = -24.3473430653209
x41 = -5.49778714378214
x42 = -96.6039740978861
x43 = 82.4668071567321
x44 = 0.785398163397448
x45 = 25.9181393921158
x46 = 98.174770424681
x47 = 57.3340659280137
x48 = -58.9048622548086
x49 = -52.621676947629
x50 = 35.3429173528852
x51 = -84.037603483527
x52 = -30.6305283725005
x53 = -36.9137136796801
x54 = -90.3207887907066
x55 = 22.776546738526
x56 = -77.7544181763474
x57 = -80.8960108299372
x58 = 88.7499924639117
x59 = -33.7721210260903
x60 = -55.7632696012188
x61 = -62.0464549083984
x62 = -43.1968989868597
x63 = 19.6349540849362
x64 = 79.3252145031423
x65 = 47.9092879672443
x66 = -74.6128255227576
x67 = 63.6172512351933
x68 = -11.7809724509617
x68 = -11.7809724509617
The graph