Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 5^x=8^x
-
Equation -27x+220=-5x
-
Equation x+12=5
-
Equation 3/(x-5)+8/x=2
- Express {x} in terms of y where:
- 12*x+1*y=15
- -16*x-10*y=4
- -4*x-20*y=10
- 19*x+6*y=8
- Derivative of:
-
sqrt(3)
- Integral of d{x}:
-
sqrt(3)
- The double integral of:
- sqrt(3)
-
Identical expressions
- two *sin(x+pi/ three)=sqrt(three)
- 2 multiply by sinus of (x plus Pi divide by 3) equally square root of (3)
- two multiply by sinus of (x plus Pi divide by three) equally square root of (three)
- 2*sin(x+pi/3)=√(3)
- 2sin(x+pi/3)=sqrt(3)
- 2sinx+pi/3=sqrt3
- 2*sin(x+pi divide by 3)=sqrt(3)
-
Similar expressions
- sqrt(x+4)=sqrt3x
- 2*sin((x+pi)/3)+cos(2*x)=sqrt(3)*cos(x)+1
- 2*sin(x-pi/3)=sqrt(3)
2*sin(x+pi/3)=sqrt(3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ pi\ ___
2*sin|x + --| = \/ 3
\ 3 /
$$2 \sin{\left(x + \frac{\pi}{3} \right)} = \sqrt{3}$$
Detail solution
Given the equation
$$2 \sin{\left(x + \frac{\pi}{3} \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{3}$$
$$x + \frac{\pi}{3} = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n$$
$$x = 2 \pi n + \frac{\pi}{3}$$
$$2 \sin{\left(x + \frac{\pi}{3} \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{3}$$
$$x + \frac{\pi}{3} = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n$$
$$x = 2 \pi n + \frac{\pi}{3}$$
Sum and product of roots
[src]
sum
pi -- 3
$$\frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
pi 0*-- 3
$$0 \frac{\pi}{3}$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -18.8495559215388
x2 = 70.162235930172
x3 = -86.9173967493176
x4 = 89.0117918517108
x5 = -17.8023583703422
x6 = 95.2949771588904
x7 = -37.6991118430775
x8 = 82.7286065445312
x9 = -56.5486677646163
x10 = 7.33038285837618
x11 = 76.4454212373516
x12 = 12.5663706143592
x13 = 32.4631240870945
x14 = -31.4159265358979
x15 = 38.7463093942741
x16 = -81.6814089933346
x17 = 94.2477796076938
x18 = 0.0
x19 = -87.9645943005142
x20 = 81.6814089933346
x21 = -75.398223686155
x22 = 62.8318530717959
x23 = -42.9350995990605
x24 = 100.530964914873
x25 = -5.23598775598299
x26 = -30.3687289847013
x27 = 75.398223686155
x28 = 6.28318530717959
x29 = -6.28318530717959
x30 = 57.5958653158129
x31 = 31.4159265358979
x32 = 25.1327412287183
x33 = 13.6135681655558
x34 = 18.8495559215388
x35 = -99.4837673636768
x36 = -94.2477796076938
x37 = 19.8967534727354
x38 = 56.5486677646163
x39 = -20589.9982516275
x40 = -93.2005820564972
x41 = -25.1327412287183
x42 = -49.2182849062401
x43 = 87.9645943005142
x44 = -24.0855436775217
x45 = -50.2654824574367
x46 = -55.5014702134197
x47 = -43.9822971502571
x48 = 50.2654824574367
x49 = 69.1150383789755
x50 = 63.8790506229925
x51 = 1037.77277323583
x52 = -74.3510261349584
x53 = -68.0678408277789
x54 = -62.8318530717959
x55 = -69.1150383789755
x56 = 1.0471975511966
x57 = 51.3126800086333
x58 = -61.7846555205993
x59 = -36.6519142918809
x60 = 37.6991118430775
x61 = -80.634211442138
x62 = -11.5191730631626
x63 = -12.5663706143592
x64 = 45.0294947014537
x65 = 106.814150222053
x66 = 26.1799387799149
x67 = 43.9822971502571
x67 = 43.9822971502571