Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation e^x=0
-
Equation x^2=10
-
Equation cos(x)=3
-
Equation x^2-3x-4=0
- Express {x} in terms of y where:
- 2*x+2*y=-6
- 7*x+20*y=-17
- 12*x+14*y=-15
- -11*x+10*y=-9
-
Identical expressions
- six *sin(x/ four -pi/ twelve)- six = zero
- 6 multiply by sinus of (x divide by 4 minus Pi divide by 12) minus 6 equally 0
- six multiply by sinus of (x divide by four minus Pi divide by twelve) minus six equally zero
- 6sin(x/4-pi/12)-6=0
- 6sinx/4-pi/12-6=0
- 6*sin(x/4-pi/12)-6=O
- 6*sin(x divide by 4-pi divide by 12)-6=0
-
Similar expressions
- 6*sin(x/4-pi/12)+6=0
- 6*sin(x/4+pi/12)-6=0
6*sin(x/4-pi/12)-6=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x pi\
6*sin|- - --| - 6 = 0
\4 12/
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} - 6 = 0$$
Detail solution
Given the equation
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} - 6 = 0$$
- this is the simplest trigonometric equation
We get:
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} = 6$$
The equation is transformed to
$$\cos{\left(\frac{x}{4} + \frac{5 \pi}{12} \right)} = -1$$
This equation is transformed to
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n + \pi$$
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n$$
, where n - is a integer
Move
$$\frac{5 \pi}{12}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{x}{4} = \pi n + \frac{7 \pi}{12}$$
$$\frac{x}{4} = \pi n - \frac{5 \pi}{12}$$
Divide both parts of the equation by
$$\frac{1}{4}$$
we get the answer:
$$x_{1} = 4 \pi n + \frac{7 \pi}{3}$$
$$x_{2} = 4 \pi n - \frac{5 \pi}{3}$$
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} - 6 = 0$$
- this is the simplest trigonometric equation
Move -6 to right part of the equation
with the change of sign in -6
We get:
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} = 6$$
Divide both parts of the equation by -6
The equation is transformed to
$$\cos{\left(\frac{x}{4} + \frac{5 \pi}{12} \right)} = -1$$
This equation is transformed to
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n + \pi$$
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n$$
, where n - is a integer
Move
$$\frac{5 \pi}{12}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{x}{4} = \pi n + \frac{7 \pi}{12}$$
$$\frac{x}{4} = \pi n - \frac{5 \pi}{12}$$
Divide both parts of the equation by
$$\frac{1}{4}$$
we get the answer:
$$x_{1} = 4 \pi n + \frac{7 \pi}{3}$$
$$x_{2} = 4 \pi n - \frac{5 \pi}{3}$$
Sum and product of roots
[src]
sum
7*pi ---- 3
$$\frac{7 \pi}{3}$$
=
7*pi ---- 3
$$\frac{7 \pi}{3}$$
product
7*pi ---- 3
$$\frac{7 \pi}{3}$$
=
7*pi ---- 3
$$\frac{7 \pi}{3}$$
7*pi/3
Numerical answer
[src]
x1 = 57.5958666500949
x2 = -68.0678390250001
x3 = 32.463124844372
x4 = 7.33038408158933
x5 = 57.5958633811658
x6 = 32.4631239639104
x7 = -68.0678428451497
x8 = -93.2005814473133
x9 = -42.9350982758384
x10 = -93.2005820590014
x11 = 82.7286054191576
x12 = 82.7286044899893
x13 = 82.7286047530984
x14 = 7.33038490934731
x15 = -42.9350990027676
x16 = 7.33038471187791
x17 = -93.2005838656637
x18 = 57.5958673787099
x19 = 32.4631229528066
x20 = 82.7286079882937
x21 = -17.8023608250547
x22 = -17.8023566054739
x23 = 107.861349234482
x24 = 57.5958633439357
x25 = -42.9351004065219
x26 = -17.8023563307113
x27 = -93.2005841085706
x28 = -68.0678392167093
x29 = -17.8023583238364
x30 = -68.0678416225784
x31 = -93.2005823421457
x32 = -42.9350975767139
x33 = 82.7286085168235
x34 = -17.8023604120996
x35 = 32.4631225830263
x36 = -42.9351008549945
x37 = 82.7286062922239
x38 = 7.330383149795
x39 = 82.7286085015994
x40 = 57.5958655582303
x41 = -68.067842646263
x42 = 7.33038322619152
x43 = 57.5958657457606
x44 = -42.9351014702332
x45 = 32.4631256206845
x46 = -68.0678407671846
x47 = 82.7286052878168
x48 = 82.7286063439891
x49 = 57.5958671046355
x50 = 32.4631230688373
x51 = 107.861345925974
x52 = -68.0678391304132
x53 = 7.33038086369274
x54 = -93.2005800960027
x55 = -93.2005806375113
x56 = 7.33038093273724
x57 = -42.9350991093679
x58 = 132.994091564363
x59 = -17.8023567520737
x60 = 7.33038256421289
x61 = 7.33038232907484
x62 = 32.463125964147
x63 = 82.7286071852077
x64 = 32.463122032436
x65 = -93.2005800826288
x66 = -68.0678387701177
x67 = 32.4631223663587
x68 = -42.9351016316325
x69 = -42.9351000077101
x70 = -68.0678423888361
x71 = 57.5958638671306
x72 = 57.5958646679633
x73 = -42.935097688124
x74 = -17.8023574989498
x75 = 32.4631260979099
x76 = -17.8023600559622
x77 = -93.2005832098587
x78 = 57.5958664351449
x79 = 7.33038150387412
x80 = 7.33038388254836
x81 = -17.8023592782964
x82 = -68.0678398450346
x83 = -17.8023600141246
x83 = -17.8023600141246