Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 1+sin(x)=0
-
Equation tg(x)=1
-
Equation x^4+4=0
-
Equation -x-4+5(x+3)=5(-1-x)-2
- Express {x} in terms of y where:
- 4*x+2*y=5
- 1*x+10*y=-18
- -18*x-2*y=9
- -11*x+9*y=-20
- Canonical form:
- 1+sin(x)
- Limit of the function:
-
1+sin(x)
- Derivative of:
-
1+sin(x)
-
Identical expressions
- one +sin(x)= zero
- 1 plus sinus of (x) equally 0
- one plus sinus of (x) equally zero
- 1+sinx=0
- 1+sin(x)=O
-
Similar expressions
- 1+sinx^4-2sinx^2+a*sinx^2-2a=1
- 1+sinx=|1-√3cosx|
- 1-sin(x)=0
- 1+sinx=0
1+sin(x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(x \right)} = -1$$
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
$$x = 2 \pi n - \frac{\pi}{2}$$
$$x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
$$\sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move 1 to right part of the equation
with the change of sign in 1
We get:
$$\sin{\left(x \right)} = -1$$
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
$$x = 2 \pi n - \frac{\pi}{2}$$
$$x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 3*pi - -- + ---- 2 2
$$- \frac{\pi}{2} + \frac{3 \pi}{2}$$
=
pi
$$\pi$$
product
-pi 3*pi ----*---- 2 2
$$- \frac{\pi}{2} \frac{3 \pi}{2}$$
=
2 -3*pi ------ 4
$$- \frac{3 \pi^{2}}{4}$$
-3*pi^2/4
Rapid solution
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
3*pi
x2 = ----
2
$$x_{2} = \frac{3 \pi}{2}$$
x2 = 3*pi/2
Numerical answer
[src]
x1 = -76.9690203748894
x2 = -39.2699084145515
x3 = -20.4203527465087
x4 = -70.6858351534454
x5 = -102.101761026058
x6 = -14.1371668370864
x7 = 17.2787599560783
x8 = 86.3937978869933
x9 = 73.8274274426229
x10 = -64.4026491641039
x11 = 23.5619437708833
x12 = -70.6858331259916
x13 = -95.818575476176
x14 = -51.8362783335234
x15 = -83.2522055723275
x16 = 92.6769830592094
x17 = -45.5530935025548
x18 = 42.4115013353669
x19 = -1.57079643188553
x20 = 10.9955739381756
x21 = -26.7035372004893
x22 = -89.5353906059052
x23 = 48.6946870830469
x24 = 98.9601682515978
x25 = -64.4026498988255
x26 = -7.85398205280014
x27 = -70.6858343571487
x28 = 48.6946866365921
x29 = -7.85398149665124
x30 = 4.7123894841958
x31 = -83.2522048211133
x32 = 4.71239022926564
x33 = 92.6769837888103
x34 = -20.420353265929
x35 = 36.1283159497235
x36 = -83.2522042893833
x37 = 54.9778710948428
x38 = -64.4026502975618
x39 = -45.5530935911043
x40 = 54.9778718908148
x41 = 61.2610571125526
x42 = -14.1371674455661
x43 = 4.71238874329685
x44 = 36.1283150875497
x45 = -95.8185758680502
x46 = -1.57079581340397
x47 = 73.8274274830848
x48 = -39.2699076683741
x49 = -7.85398119154045
x50 = 73.8274268520838
x51 = 80.1106130902139
x52 = 29.8451297031011
x53 = -20.4203520060805
x54 = -89.535390750197
x55 = -58.1194639976905
x56 = -14.1371667858125
x57 = -32.9867224188086
x58 = -76.9690195738024
x59 = 80.1106131368654
x60 = 17.2787591562062
x61 = 538.783139388541
x62 = -1.57079639503667
x63 = 67.54424230971
x64 = 48.6946873020308
x65 = 29.8451303231501
x66 = 67.5442415586719
x67 = -45.5530929624673
x68 = -51.8362791922783
x69 = 42.4115007274741
x70 = -58.1194645939029
x71 = -89.5353901118113
x72 = 48.6946859012172
x73 = 10.9955747360645
x74 = 36.1283157235346
x75 = 92.6769843439965
x76 = 29.845130330036
x77 = -95.8185763308148
x78 = 67.5442408278864
x79 = -26.7035379986821
x80 = -39.2699069219675
x81 = 98.9601690454399
x82 = 23.5619444059921
x83 = -32.9867232184024
x84 = -58.1194639046052
x85 = 42.4115007162407
x86 = 98.9601692809083
x87 = 61.2610563112167
x88 = 23.5619451518571
x89 = 80.1106122287081
x90 = -51.8362786893284
x91 = 86.3937984838325
x92 = 86.3937978309099
x92 = 86.3937978309099
The graph