Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x)=1
-
Equation cos(x)=1/3
-
Equation k^2-4*k+13=0
-
Equation k^2-4*k+3=0
- Express {x} in terms of y where:
- -14*x+1*y=3
- -11*x+4*y=-8
- 16*x+7*y=8
- 17*x-11*y=2
- Sum of series:
- sinx
- Graphing y =:
- sinx
- Integral of d{x}:
-
sinx
-
Identical expressions
- sinx=sqrt3/ two
- sinus of x equally square root of 3 divide by 2
- sinus of x equally square root of 3 divide by two
- sinx=√3/2
- sinx=sqrt3 divide by 2
-
Similar expressions
- sqrt(3)/2*cos(x)-1/2*sin(x)=1
- sin(x+(3pi/4))=0
- sin(x)+sqrt(((2-sqrt(3))/2)(cos(x)+1))=0
- cos(x)=-sqrt(3)/2
- sin(x)=1
sinx=sqrt3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Rapid solution
[src]
pi
x_1 = --
3
$$x_{1} = \frac{\pi}{3}$$
2*pi
x_2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
Sum and product of roots
[src]
sum
pi 2*pi -- + ---- 3 3
$$\left(\frac{\pi}{3}\right) + \left(\frac{2 \pi}{3}\right)$$
=
pi
$$\pi$$
product
pi 2*pi -- * ---- 3 3
$$\left(\frac{\pi}{3}\right) * \left(\frac{2 \pi}{3}\right)$$
=
2 2*pi ----- 9
$$\frac{2 \pi^{2}}{9}$$
Numerical answer
[src]
x1 = -67.0206432765823
x2 = 33.5103216382911
x3 = -23.0383461263252
x4 = -10.471975511966
x5 = -93.2005820564972
x6 = 76.4454212373516
x7 = 63.8790506229925
x8 = 90.0589894029074
x9 = 82.7286065445312
x10 = 146.607657167524
x11 = -61.7846555205993
x12 = 1188.56922060814
x13 = -17.8023583703422
x14 = 26.1799387799149
x15 = 38.7463093942741
x16 = 944.572191179331
x17 = 8.37758040957278
x18 = -41.8879020478639
x19 = -79.5870138909414
x20 = -80.634211442138
x21 = 2.0943951023932
x22 = 240.855436775217
x23 = 32.4631240870945
x24 = -11.5191730631626
x25 = 19.8967534727354
x26 = -74.3510261349584
x27 = -55.5014702134197
x28 = -73.3038285837618
x29 = 27.2271363311115
x30 = 70.162235930172
x31 = 58.6430628670095
x32 = -104.71975511966
x33 = 209.43951023932
x34 = 39.7935069454707
x35 = 95.2949771588904
x36 = -86.9173967493176
x37 = 71.2094334813686
x38 = 1.0471975511966
x39 = 52.3598775598299
x40 = 101.57816246607
x41 = 77.4926187885482
x42 = 13.6135681655558
x43 = -92.1533845053006
x44 = -49.2182849062401
x45 = 57.5958653158129
x46 = -613.657765001206
x47 = -112.050137978036
x48 = -68.0678408277789
x49 = 20.943951023932
x50 = 83.7758040957278
x51 = -30.3687289847013
x52 = 14.6607657167524
x53 = -29.3215314335047
x54 = 46.0766922526503
x55 = -36.6519142918809
x56 = 170.693200845045
x57 = -42.9350995990605
x58 = -4.18879020478639
x59 = -85.870199198121
x60 = -60.7374579694027
x61 = -99.4837673636768
x62 = 51.3126800086333
x63 = -54.4542726622231
x64 = -5.23598775598299
x65 = -48.1710873550435
x66 = -98.4365698124802
x67 = 96.342174710087
x68 = -16.7551608191456
x69 = 45.0294947014537
x70 = -520.457182944709
x71 = -6607.81654805053
x72 = 7.33038285837618
x73 = -24.0855436775217
x74 = 64.9262481741891
x75 = -35.6047167406843
x76 = 195.825942073764
x77 = 89.0117918517108
x77 = 89.0117918517108
The graph