Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)=-sqrt(3)/2
- Equation x^2-14/x-10x/x^2-14=3
-
Equation sin^3x+cos^3x=1
- Equation Cx-1^x*(x-1)=30
- Express {x} in terms of y where:
- 9*x+18*y=6
- 15*x-15*y=16
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- Derivative of:
-
sin(x)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)=-sqrt(three)/ two
- sinus of (x) equally minus square root of (3) divide by 2
- sinus of (x) equally minus square root of (three) divide by two
- sin(x)=-√(3)/2
- sinx=-sqrt3/2
- sin(x)=-sqrt(3) divide by 2
-
Similar expressions
- sin2x=-(sqrt3/2)
- sin5xcos3x-cos5xsin3x=-(sqrt(3)/2)
- sin(x)=+sqrt(3)/2
- sin(0.5x)=-sqrt3/2
- sin(3x)=-sqrt3/2
- cos(x/3)*cos(Pi/6)+sin(x/3)*sin(Pi/6)=-1
- (cos2x+sinx)/sqrt(sin(x-pi/4))=0
- sinx=-sqrt(3)/2
sin(x)=-sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
sin(x) = -------
2
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- 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
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- 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
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Rapid solution
[src]
-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
4*pi
x2 = ----
3
$$x_{2} = \frac{4 \pi}{3}$$
Sum and product of roots
[src]
sum
pi 4*pi
0 - -- + ----
3 3
$$\left(- \frac{\pi}{3} + 0\right) + \frac{4 \pi}{3}$$
=
pi
$$\pi$$
product
-pi 4*pi 1*----*---- 3 3
$$\frac{4 \pi}{3} \cdot 1 \left(- \frac{\pi}{3}\right)$$
=
2 -4*pi ------ 9
$$- \frac{4 \pi^{2}}{9}$$
-4*pi^2/9
Numerical answer
[src]
x1 = -90.0589894029074
x2 = 93.2005820564972
x3 = -1559.27715373173
x4 = 42.9350995990605
x5 = 54.4542726622231
x6 = -46.0766922526503
x7 = -52.3598775598299
x8 = -39.7935069454707
x9 = -63.8790506229925
x10 = 11.5191730631626
x11 = 393.746279249921
x12 = 67.0206432765823
x13 = -11851.1346868919
x14 = 80.634211442138
x15 = -57.5958653158129
x16 = 74.3510261349584
x17 = -5606.69568910658
x18 = -1.0471975511966
x19 = 5.23598775598299
x20 = 17.8023583703422
x21 = 99.4837673636768
x22 = -27.2271363311115
x23 = -51.3126800086333
x24 = -32.4631240870945
x25 = 79.5870138909414
x26 = -151.843644923507
x27 = -96.342174710087
x28 = -26.1799387799149
x29 = -101.57816246607
x30 = -13.6135681655558
x31 = 30.3687289847013
x32 = -2.0943951023932
x33 = -82.7286065445312
x34 = -76.4454212373516
x35 = 24.0855436775217
x36 = 49.2182849062401
x37 = 16.7551608191456
x38 = 86.9173967493176
x39 = 23.0383461263252
x40 = 48.1710873550435
x41 = -14.6607657167524
x42 = -71.2094334813686
x43 = -20.943951023932
x44 = -89.0117918517108
x45 = 35.6047167406843
x46 = -8.37758040957278
x47 = 36.6519142918809
x48 = 98.4365698124802
x49 = -70.162235930172
x50 = -19.8967534727354
x51 = 85.870199198121
x52 = 92.1533845053006
x53 = -45.0294947014537
x54 = 68.0678408277789
x55 = -77.4926187885482
x56 = -58.6430628670095
x57 = -64.9262481741891
x58 = 61.7846555205993
x59 = 10.471975511966
x60 = 29.3215314335047
x61 = -7.33038285837618
x62 = 73.3038285837618
x63 = 60.7374579694027
x64 = -33.5103216382911
x65 = -114.144533080429
x66 = 4.18879020478639
x67 = -95.2949771588904
x68 = 55.5014702134197
x69 = 41.8879020478639
x70 = -83.7758040957278
x71 = -38.7463093942741
x71 = -38.7463093942741
The graph