Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3x^2+4x=0
-
Equation 5x(x-4)-x(3+5x)=4
-
Equation (x+6)^2=(x-7)^2
- Equation x^2-289=0
- Express {x} in terms of y where:
- 10*x+9*y=-4
- -15*x-19*y=2
- -11*x-14*y=-19
- -17*x-15*y=-17
- Graphing y =:
-
tan(x)
- Derivative of:
-
tan(x)
- Integral of d{x}:
-
tan(x)
-
Identical expressions
- tan(x)=root3/ two
- tangent of (x) equally root3 divide by 2
- tangent of (x) equally root3 divide by two
- tanx=root3/2
- tan(x)=root3 divide by 2
-
Similar expressions
- tan(x-pi/4)=(-1)/sqrt(3)
tan(x)=root3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
, where n - is a integer
$$\tan{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
, where n - is a integer
Rapid solution
[src]
/ ___\
|\/ 3 |
x_1 = atan|-----|
\ 2 /
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
Sum and product of roots
[src]
sum
/ ___\
|\/ 3 |
atan|-----|
\ 2 /
$$\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}\right)$$
=
/ ___\
|\/ 3 |
atan|-----|
\ 2 /
$$\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
product
/ ___\
|\/ 3 |
atan|-----|
\ 2 /
$$\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}\right)$$
=
/ ___\
|\/ 3 |
atan|-----|
\ 2 /
$$\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}$$
Numerical answer
[src]
x1 = 25.8464656076631
x2 = 47.8376141827917
x3 = 19.5632803004835
x4 = 3.85531703253456
x5 = 32.1296509148427
x6 = 35.2712435684325
x7 = 22.7048729540733
x8 = -90.3924625751592
x9 = 16.4216876468937
x10 = -8.71105358182461
x11 = -43.2685727713123
x12 = 69.8287627579202
x13 = -2.42786827464503
x14 = -33.843794810543
x15 = 63.5455774507406
x16 = 88.678318679459
x17 = -80.9676846143899
x18 = 91.8199113330488
x19 = -65.2597213464409
x20 = -5.56946092823482
x21 = -52.6933507320817
x22 = -14.9942388890042
x23 = -55.8349433856715
x24 = 82.3951333722794
x25 = -18.135831542594
x26 = 50.9792068363815
x27 = -30.7022021569532
x28 = 6.99690968612435
x29 = 98.1030966402284
x30 = -96.6756478823388
x31 = -40.1269801177225
x32 = 54.1207994899712
x33 = -21.2774241961838
x34 = -58.9765360392613
x35 = -27.5606095033634
x36 = 57.262392143561
x37 = 85.5367260258692
x38 = -87.2508699215694
x39 = 13.2800949933039
x40 = 60.4039847971508
x41 = -49.5517580784919
x42 = 41.5544288756121
x43 = -24.4190168497736
x44 = 0.713724378944766
x45 = -93.534055228749
x46 = -46.4101654249021
x47 = -71.5429066536205
x48 = -11.8526462354144
x49 = -99.8172405359286
x50 = 28.9880582612529
x51 = 101.244689293818
x52 = 76.1119480650998
x53 = 44.6960215292019
x54 = 38.4128362220223
x55 = 10.1385023397141
x56 = 94.9615039866386
x57 = -68.4013140000307
x58 = -62.1181286928511
x59 = 72.97035541151
x60 = -36.9853874641328
x61 = 79.2535407186896
x62 = -84.1092772679796
x63 = -77.8260919608001
x64 = 66.6871701043304
x65 = -74.6844993072103
x65 = -74.6844993072103
The graph