Mister Exam
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How to use it?
- Equation:
-
Equation 17x+2x^2+21=0
- Equation 4*x^3-19*x^2+19*x+6=0
-
Equation tgx+tg2x=tg3x
- Equation cos^2((2*pi/3)-x)=cos^2((2*pi/3)+x)
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 9*x+18*y=6
- 15*x-15*y=16
- Graphing y =:
- tg3x
- Derivative of:
-
tg3x
- Integral of d{x}:
-
tg3x
-
Identical expressions
- tgx+tg2x=tg3x
- tgx plus tg2x equally tg3x
-
Similar expressions
- arcctg(3x^2-1)=arcctg(2x^2+x+1)
- tg^3x-tg^2x-3tgx+3=0
- tgx-tg2x=tg3x
- tg(3x+(pi)/6)=1
tgx+tg2x=tg3x equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
tan(x) + tan(2*x) = tan(3*x)
$$\tan{\left(x \right)} + \tan{\left(2 x \right)} = \tan{\left(3 x \right)}$$
Sum and product of roots
[src]
sum
-2*pi -pi pi 2*pi
0 + ----- + ---- + -- + ---- + pi
3 3 3 3
$$\left(0\right) + \left(- \frac{2 \pi}{3}\right) + \left(- \frac{\pi}{3}\right) + \left(\frac{\pi}{3}\right) + \left(\frac{2 \pi}{3}\right) + \left(\pi\right)$$
=
pi
$$\pi$$
product
-2*pi -pi pi 2*pi
0 * ----- * ---- * -- * ---- * pi
3 3 3 3
$$\left(0\right) * \left(- \frac{2 \pi}{3}\right) * \left(- \frac{\pi}{3}\right) * \left(\frac{\pi}{3}\right) * \left(\frac{2 \pi}{3}\right) * \left(\pi\right)$$
=
0
$$0$$
Rapid solution
[src]
x_1 = 0
$$x_{1} = 0$$
-2*pi
x_2 = -----
3
$$x_{2} = - \frac{2 \pi}{3}$$
-pi
x_3 = ----
3
$$x_{3} = - \frac{\pi}{3}$$
pi
x_4 = --
3
$$x_{4} = \frac{\pi}{3}$$
2*pi
x_5 = ----
3
$$x_{5} = \frac{2 \pi}{3}$$
x_6 = pi
$$x_{6} = \pi$$
Numerical answer
[src]
x1 = 85.870199198121
x2 = 80.634211442138
x3 = 6.28317662778413
x4 = 40.8406447330932
x5 = 52.3598775598299
x6 = -85.870199198121
x7 = -59.690276049124
x8 = -52.3598775598299
x9 = -11.5191730631626
x10 = -4.18879020478639
x11 = -15.7079742594227
x12 = 21.9911516443743
x13 = -87.9646061403382
x14 = -65.9734547790939
x15 = -63.8790506229925
x16 = -39.7935069454707
x17 = -2.0943951023932
x18 = -41.8879020478639
x19 = 46.0766922526503
x20 = 65.9734548782878
x21 = 70.162235930172
x22 = 94.2477801894998
x23 = -21.9911516431803
x24 = -37.6991251504123
x25 = -72.2566270462168
x26 = 98.4365698124802
x27 = 68.0678408277789
x28 = -46.0766922526503
x29 = -43.982303253589
x30 = -79.5870138909414
x31 = 43.982303272884
x32 = 96.342174710087
x33 = -26.1799387799149
x34 = -57.5958653158129
x35 = 63.8790506229925
x36 = -74.3510261349584
x37 = 8.37758040957278
x38 = 83.7758040957278
x39 = 72.2566292952887
x40 = -61.7846555205993
x41 = 30.3687289847013
x42 = -96.342174710087
x43 = 36.6519142918809
x44 = 2.0943951023932
x45 = 14.6607657167524
x46 = 0.0
x47 = 48.1710873550435
x48 = -83.7758040957278
x49 = 24.0855436775217
x50 = 58.6430628670095
x51 = 28.2743275145522
x52 = -19.8967534727354
x53 = 26.1799387799149
x54 = -68.0678408277789
x55 = 19.8967534727354
x56 = 41.8879020478639
x57 = -81.6814269599112
x58 = -13.6135681655558
x59 = -24.0855436775217
x60 = 32.4631240870945
x61 = 4.18879020478639
x62 = -35.6047167406843
x63 = 76.4454212373516
x64 = 74.3510261349584
x65 = 90.0589894029074
x66 = 92.1533845053006
x67 = -90.0589894029074
x68 = -30.3687289847013
x69 = 87.9646064597778
x70 = -7.33038285837618
x71 = -17.8023583703422
x72 = 50.2654784033431
x72 = 50.2654784033431
The graph