Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation 1-y^2=2+x
-
Equation x^2=-16
-
Equation sin(x)=-1
-
Equation z^4+1=0
- Express {x} in terms of y where:
- 20*x+6*y=8
- -7*x+7*y=-14
- 1*x-4*y=1
- 16*x-17*y=-9
- Derivative of:
-
sin(x)
-
-1
- Integral of d{x}:
-
sin(x)
-
-1
- Canonical form:
- sin(x)
- Sum of series:
-
-1
-
Identical expressions
- sin(x)=- one
- sinus of (x) equally minus 1
- sinus of (x) equally minus one
- sinx=-1
-
Similar expressions
- sin(x)=+1
- sinx-cosx=1/2
- (1+sinx)(1+cosx)=1+sinx+cosx
- sinx=-1
sin(x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
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
$$\sin{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
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 = 10.9955747360645
x2 = 29.845130330036
x3 = -89.535390750197
x4 = 42.4115007274741
x5 = 80.1106130902139
x6 = 73.8274274830848
x7 = -32.9867224188086
x8 = 48.6946866365921
x9 = -14.1371667858125
x10 = 36.1283157235346
x11 = -20.420353265929
x12 = -39.2699076683741
x13 = 92.6769837888103
x14 = 67.54424230971
x15 = -26.7035379986821
x16 = -64.4026502975618
x17 = -83.2522048211133
x18 = -51.8362786893284
x19 = 86.3937984838325
x20 = -102.101761026058
x21 = -7.85398149665124
x22 = 54.9778710948428
x23 = 80.1106131368654
x24 = 67.5442408278864
x25 = -7.85398119154045
x26 = 61.2610563112167
x27 = 86.3937978309099
x28 = -83.2522042893833
x29 = 98.9601692809083
x30 = -89.5353901118113
x31 = -64.4026498988255
x32 = 92.6769830592094
x33 = -58.1194645939029
x34 = 36.1283159497235
x35 = 48.6946873020308
x36 = -83.2522055723275
x37 = 4.71238874329685
x38 = 98.9601682515978
x39 = -45.5530929624673
x40 = -14.1371668370864
x41 = 4.7123894841958
x42 = -1.57079639503667
x43 = -70.6858343571487
x44 = -95.8185758680502
x45 = 36.1283150875497
x46 = 86.3937978869933
x47 = 4.71239022926564
x48 = -95.818575476176
x49 = -7.85398205280014
x50 = 29.8451303231501
x51 = -70.6858331259916
x52 = -20.4203520060805
x53 = 48.6946870830469
x54 = -39.2699069219675
x55 = 42.4115013353669
x56 = -39.2699084145515
x57 = 23.5619437708833
x58 = 10.9955739381756
x59 = -1.57079643188553
x60 = 61.2610571125526
x61 = -70.6858351534454
x62 = 42.4115007162407
x63 = -51.8362791922783
x64 = -20.4203527465087
x65 = 73.8274274426229
x66 = -51.8362783335234
x67 = 48.6946859012172
x68 = 80.1106122287081
x69 = 92.6769843439965
x70 = 98.9601690454399
x71 = -14.1371674455661
x72 = 538.783139388541
x73 = -76.9690195738024
x74 = -26.7035372004893
x75 = -45.5530935025548
x76 = 73.8274268520838
x77 = -45.5530935911043
x78 = 23.5619444059921
x79 = -95.8185763308148
x80 = -32.9867232184024
x81 = -89.5353906059052
x82 = 23.5619451518571
x83 = 29.8451297031011
x84 = 67.5442415586719
x85 = -76.9690203748894
x86 = -64.4026491641039
x87 = 54.9778718908148
x88 = -58.1194639976905
x89 = -58.1194639046052
x90 = 17.2787599560783
x91 = -1.57079581340397
x92 = 17.2787591562062
x92 = 17.2787591562062
The graph