Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+4*x+4=0
-
Equation (x^2-4)^2+(x^2-3x-10)^2=0
-
Equation -x/3+x+7=3
-
Equation -20*(x-13)=-220
- Express {x} in terms of y where:
- -14*x+4*y=-16
- -13*x-10*y=5
- 9*x-1*y=17
- -12*x-8*y=13
- Integral of d{x}:
- sin(x+(pi/3))
- Limit of the function:
-
sqrt(2)/2
- sqrt(2)/2
-
Identical expressions
- sin(x+(pi/ three))=sqrt(two)/ two
- sinus of (x plus ( Pi divide by 3)) equally square root of (2) divide by 2
- sinus of (x plus ( Pi divide by three)) equally square root of (two) divide by two
- sin(x+(pi/3))=√(2)/2
- sinx+pi/3=sqrt2/2
- sin(x+(pi divide by 3))=sqrt(2) divide by 2
-
Similar expressions
- 2*sin(x+pi/3)-sqrt(3*cos(2*x))=sin(x)+sqrt(3)
- 2*sin(x+pi/3)=sqrt(3)
- tg(5x)=sqrt2/2
- 4*sin(x+pi/3)+cos(2*x+2*pi/3)=5/2
- sin(x-(pi/3))=sqrt(2)/2
- 3*ctg(pi/3)*sin(x+pi/3)-sqrt(3)=0
sin(x+(pi/3))=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ / pi\ \/ 2 sin|x + --| = ----- \ 3 / 2
$$\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{4}$$
$$x + \frac{\pi}{3} = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n - \frac{\pi}{12}$$
$$x = 2 \pi n + \frac{5 \pi}{12}$$
$$\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{4}$$
$$x + \frac{\pi}{3} = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n - \frac{\pi}{12}$$
$$x = 2 \pi n + \frac{5 \pi}{12}$$
Rapid solution
[src]
-pi
x1 = ----
12
$$x_{1} = - \frac{\pi}{12}$$
5*pi
x2 = ----
12
$$x_{2} = \frac{5 \pi}{12}$$
x2 = 5*pi/12
Sum and product of roots
[src]
sum
pi 5*pi - -- + ---- 12 12
$$- \frac{\pi}{12} + \frac{5 \pi}{12}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
-pi 5*pi ----*---- 12 12
$$- \frac{\pi}{12} \frac{5 \pi}{12}$$
=
2 -5*pi ------ 144
$$- \frac{5 \pi^{2}}{144}$$
-5*pi^2/144
Numerical answer
[src]
x1 = 56.2868683768171
x2 = -55.2396708256205
x3 = 31.1541271480988
x4 = 81.4196096055355
x5 = 18.5877565337396
x6 = -25.3945406165175
x7 = 70.4240353179712
x8 = 75.1364242983559
x9 = 45.2912940892529
x10 = -30.1069295969022
x11 = -74.0892267471593
x12 = 12.30457122656
x13 = 100.269165527074
x14 = 39.0081087820733
x15 = -80.3724120543389
x16 = -69.3768377667746
x17 = 50.0036830696375
x18 = -11.2573736753634
x19 = -56.8104671524154
x20 = 57.857664703612
x21 = 8639.11799798413
x22 = 87.7027949127151
x23 = -36.3901149040818
x24 = -19.1113553093379
x25 = -281.434341884086
x26 = 26.4417381677141
x27 = -94.5095789954929
x28 = -17.540558982543
x29 = -4.97418836818384
x30 = -92.9387826686981
x31 = 82.9904059323304
x32 = 89.27359123951
x33 = -88.2263936883134
x34 = -44.2440965380563
x35 = 7.59218224617533
x36 = 6.02138591938044
x37 = -75.6600230739542
x38 = 24.8709418409192
x39 = -23.8237442897226
x40 = -86.6555973615185
x41 = -67.8060414399797
x42 = -37.9609112308767
x43 = -12.8281700021583
x44 = -48.9564855184409
x45 = -0.261799387799149
x46 = 95.5567765466895
x47 = -42.6733002112614
x48 = 1.30899693899575
x49 = 20.1585528605345
x50 = -50.5272818452358
x51 = 43.720497762458
x52 = 68.8532389911763
x53 = 13.8753675533549
x54 = 32.7249234748937
x55 = 37.4373124552784
x56 = 51.5744793964324
x57 = 64.1408500107916
x58 = 62.5700536839967
x59 = -6.54498469497874
x60 = -31.6777259236971
x61 = -81.9432083811338
x62 = -61.5228561328001
x63 = 93.9859802198946
x64 = -63.093652459595
x65 = 108.123147161049
x66 = -99.2219679758776
x67 = 76.7072206251508
x67 = 76.7072206251508