Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 10x-11=4x-7
-
Equation x^3+30x^2+300x+1008=0
- Equation x^2+196=0
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Equation cos(x+pi/2)=sqrt(3)/2
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- Integral of d{x}:
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cos(x+pi/2)
- Derivative of:
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sqrt(3)/2
- Limit of the function:
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sqrt(3)/2
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Identical expressions
- cos(x+pi/ two)=sqrt(three)/ two
- co sinus of e of (x plus Pi divide by 2) equally square root of (3) divide by 2
- co sinus of e of (x plus Pi divide by two) equally square root of (three) divide by two
- cos(x+pi/2)=√(3)/2
- cosx+pi/2=sqrt3/2
- cos(x+pi divide by 2)=sqrt(3) divide by 2
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Similar expressions
- tg(x)=sqrt3/2
- sin(0.5x)=-sqrt3/2
- sin2x=-(sqrt3/2)
- cos(x-pi/2)=sqrt(3)/2
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What you mean?
- cos((x + pi)/2) = sqrt(3)/2
- cos(x + pi/2) = sqrt(3)/2
- cos(x + pi/2) = sqrt(3)/2
You entered:
cos(x+pi/2)=sqrt(3)/2
What you mean?
cos(x+pi/2)=sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ / pi\ \/ 3 cos|x + --| = ----- \ 2 / 2
$$\cos{\left(x + \frac{\pi}{2} \right)} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\cos{\left(x + \frac{\pi}{2} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
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
$$\cos{\left(x + \frac{\pi}{2} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
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
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
Rapid solution
[src]
-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
4*pi
x2 = ----
3
$$x_{2} = \frac{4 \pi}{3}$$
Numerical answer
[src]
x1 = 35.6047167406843
x2 = 86.9173967493176
x3 = -51.3126800086333
x4 = 68.0678408277789
x5 = 98.4365698124802
x6 = 85.870199198121
x7 = 67.0206432765823
x8 = 10.471975511966
x9 = 54.4542726622231
x10 = 11.5191730631626
x11 = -7.33038285837618
x12 = 41.8879020478639
x13 = -58.6430628670095
x14 = -151.843644923507
x15 = -45.0294947014537
x16 = -26.1799387799149
x17 = 48.1710873550435
x18 = 5.23598775598299
x19 = -11851.1346868919
x20 = -83.7758040957278
x21 = 73.3038285837618
x22 = 4.18879020478639
x23 = 36.6519142918809
x24 = -70.162235930172
x25 = 49.2182849062401
x26 = -101.57816246607
x27 = 92.1533845053006
x28 = -95.2949771588904
x29 = -46.0766922526503
x30 = 17.8023583703422
x31 = -71.2094334813686
x32 = -77.4926187885482
x33 = -13.6135681655558
x34 = 61.7846555205993
x35 = -2.0943951023932
x36 = -32.4631240870945
x37 = -38.7463093942741
x38 = -39.7935069454707
x39 = -82.7286065445312
x40 = 99.4837673636768
x41 = -64.9262481741891
x42 = 93.2005820564972
x43 = 24.0855436775217
x44 = -33.5103216382911
x45 = 23.0383461263252
x46 = 30.3687289847013
x47 = -76.4454212373516
x48 = -1.0471975511966
x49 = -114.144533080429
x50 = -1559.27715373173
x51 = 29.3215314335047
x52 = 60.7374579694027
x53 = -19.8967534727354
x54 = -96.342174710087
x55 = -27.2271363311115
x56 = -52.3598775598299
x57 = 79.5870138909414
x58 = -5606.69568910658
x59 = 42.9350995990605
x60 = -8.37758040957278
x61 = -57.5958653158129
x62 = -89.0117918517108
x63 = 55.5014702134197
x64 = -63.8790506229925
x65 = 16.7551608191456
x66 = 393.746279249921
x67 = -20.943951023932
x68 = 74.3510261349584
x69 = -90.0589894029074
x70 = -14.6607657167524
x71 = 80.634211442138
x71 = 80.634211442138
The graph