Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 7*x=0
-
Equation 3x-2=x+4
-
Equation tan(x)=7
-
Equation (x-3)(x^2-2x+1)=3(x-1)
- Express {x} in terms of y where:
- 18*x-10*y=-9
- 18*x-12*y=-9
- 12*x+11*y=20
- 19*x-12*y=-9
- Derivative of:
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sqrt(3)
- Integral of d{x}:
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sqrt(3)
- The double integral of:
- sqrt(3)
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Identical expressions
- three *tan(x/ two)=sqrt(three)
- 3 multiply by tangent of (x divide by 2) equally square root of (3)
- three multiply by tangent of (x divide by two) equally square root of (three)
- 3*tan(x/2)=√(3)
- 3tan(x/2)=sqrt(3)
- 3tanx/2=sqrt3
- 3*tan(x divide by 2)=sqrt(3)
3*tan(x/2)=sqrt(3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$3 \tan{\left(\frac{x}{2} \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(\frac{x}{2} \right)} = \frac{\sqrt{3}}{3}$$
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{3}$$
$$3 \tan{\left(\frac{x}{2} \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 3
The equation is transformed to
$$\tan{\left(\frac{x}{2} \right)} = \frac{\sqrt{3}}{3}$$
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{3}$$
Sum and product of roots
[src]
sum
pi -- 3
$$\frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
pi -- 3
$$\frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
pi/3
Numerical answer
[src]
x1 = -24.0855436775217
x2 = 32.4631240870945
x3 = 26.1799387799149
x4 = -42.9350995990605
x5 = -68.0678408277789
x6 = 19.8967534727354
x7 = 45.0294947014537
x8 = -86.9173967493176
x9 = 57.5958653158129
x10 = 7.33038285837618
x11 = 95.2949771588904
x12 = -30.3687289847013
x13 = 38.7463093942741
x14 = 82.7286065445312
x15 = 1.0471975511966
x16 = -5.23598775598299
x17 = -93.2005820564972
x18 = -11.5191730631626
x19 = -74.3510261349584
x20 = 76.4454212373516
x21 = -80.634211442138
x22 = -17.8023583703422
x23 = 89.0117918517108
x24 = 101.57816246607
x25 = -55.5014702134197
x26 = 63.8790506229925
x27 = -99.4837673636768
x28 = 51.3126800086333
x29 = -49.2182849062401
x30 = -36.6519142918809
x31 = 13.6135681655558
x32 = 70.162235930172
x33 = -61.7846555205993
x33 = -61.7846555205993