Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
-
Equation (x-11)*(-x+9)=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
- Integral of d{x}:
- (1-sinx)
-
Identical expressions
- (one -sinx)
- (1 minus sinus of x)
- (one minus sinus of x)
- 1-sinx
-
Similar expressions
- 2*sqrt((cos(x))^2)-sqrt(1-(sin(x))^2)+cos(x)=0
- tg(x)-sin(x)*tg(x)=1-sin(x)
- 1*(-sin(x)-i*cos(x))=0
- (2*cos(x)-sqrt(3))/(1-sin(x)^(2))*(1)-sin(x)=0
- (cos*x-sqrt2\2)(1-sin*)x=0
- (1+sinx)
(1-sinx) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$1 - \sin{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$- \sin{\left(x \right)} = -1$$
The equation is transformed to
$$\sin{\left(x \right)} = 1$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{2}$$
$$x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
$$1 - \sin{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
Move 1 to right part of the equation
with the change of sign in 1
We get:
$$- \sin{\left(x \right)} = -1$$
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(x \right)} = 1$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{2}$$
$$x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
pi/2
Numerical answer
[src]
x1 = 39.2699077336963
x2 = -77664.8827844698
x3 = 70.6858358251975
x4 = -98.9601681513438
x5 = -42.4115005850814
x6 = -92.6769837307794
x7 = 51.8362788867584
x8 = 39.2699085343272
x9 = 70.6858344802043
x10 = -42.4115013226904
x11 = -86.3937988139119
x12 = -23.5619450115115
x13 = 14.1371671100222
x14 = 58.1194636580315
x15 = -4.71238862219396
x16 = -61.2610562447228
x17 = -23.5619449492902
x18 = 76.9690196732095
x19 = 26.7035387715281
x20 = 1.57079582971902
x21 = 95.8185760629547
x22 = -67.5442420547782
x23 = -17.2787583315643
x24 = 95.8185764110282
x25 = -29.8451297624452
x26 = 51.8362789031518
x27 = 76.9690204681432
x28 = -42.4115017818136
x29 = -17.2787590920677
x30 = -48.6946865760795
x31 = -67.5442421706656
x32 = -54.9778709962906
x33 = -73.8274269047688
x34 = 83.2522056907544
x35 = 32.9867233134552
x36 = -36.1283160197768
x37 = 70.6858352127237
x38 = -17.2787598356363
x39 = 45.553093730794
x40 = -92.6769829355125
x41 = 45.5530922954328
x42 = 1.57079769954017
x43 = 64.4026493072124
x44 = -36.1283153448593
x45 = 20.420352160156
x46 = -61.2610555612794
x47 = -10.9955746401247
x48 = 3017.49974516717
x49 = 20.4203527610188
x50 = -48.6946857788076
x51 = -86.3937984749131
x52 = -36.1283154173375
x53 = 26.7035380604159
x54 = 51.8362782775539
x55 = 1.57079525114023
x56 = 89.535390888605
x57 = 58.119464520069
x58 = 45.5530929823099
x59 = 95.8185754266891
x60 = 7.85398177249874
x61 = -54.9778717966574
x62 = -4.71238942125338
x63 = 7.85398174307326
x64 = 14.1371673791846
x65 = 1.57079657289894
x66 = -67.5442415371049
x67 = -29.8451306226524
x68 = -29.8451300954883
x69 = 20.4203521477756
x70 = 89.5353901350773
x71 = 58.1194643979608
x72 = 95.8185759975842
x73 = 83.252204888767
x74 = -10.9955738413568
x75 = 26.703537322248
x76 = 14.1371665172699
x77 = 32.9867225164981
x78 = 89.5353893728458
x79 = -86.3937977431483
x80 = -80.1106125781572
x81 = -73.8274277616689
x82 = -98.9601689530982
x83 = -23.5619443878998
x84 = 102.101760799573
x85 = 7.85398112872719
x86 = -61.2610569934486
x87 = 64.4026499096387
x88 = -73.8274272798455
x89 = -80.1106124650157
x90 = -80.1106131679426
x91 = 64.4026492731727
x91 = 64.4026492731727