Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tg^2(4x)+tg(4x)=0.
-
Equation z^8-1=0
-
Equation 16x+5x^2+12=0
- Equation 7x^2+6x-9=-x^2+14-3
- Express {x} in terms of y where:
- 60x^2y+75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- (x-17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
- 5*x-5*y=20
- 8*x-7*y=-13
-
Identical expressions
- tg^ two (4x)+tg(4x)= zero .
- tg squared (4x) plus tg(4x) equally 0.
- tg to the power of two (4x) plus tg(4x) equally zero .
- tg2(4x)+tg(4x)=0.
- tg24x+tg4x=0.
- tg²(4x)+tg(4x)=0.
- tg to the power of 2(4x)+tg(4x)=0.
- tg^24x+tg4x=0.
- tg^2(4x)+tg(4x)=O.
-
Similar expressions
- tg^2(4x)-tg(4x)=0.
tg^2(4x)+tg(4x)=0. equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 tan (4*x) + tan(4*x) = 0
$$\tan^{2}{\left(4 x \right)} + \tan{\left(4 x \right)} = 0$$
Detail solution
Given the equation:
$$\tan^{2}{\left(4 x \right)} + \tan{\left(4 x \right)} = 0$$
Transform
$$\tan^{2}{\left(4 x \right)} + \tan{\left(4 x \right)} = 0$$
$$\left(\tan{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} = 0$$
Consider each factor separately
$$\tan{\left(4 x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$\tan{\left(4 x \right)} = -1$$
This equation is transformed to
$$4 x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$4 x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
get the intermediate answer:
$$x = \frac{\pi n}{4} - \frac{\pi}{16}$$
$$\tan{\left(4 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(4 x \right)} = 0$$
This equation is transformed to
$$4 x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$4 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
get the intermediate answer:
$$x = \frac{\pi n}{4} - \frac{\pi}{16}$$
$$x = \frac{\pi n}{4}$$
The final answer:
$$x_{1} = \frac{\pi n}{4} - \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{4}$$
$$\tan^{2}{\left(4 x \right)} + \tan{\left(4 x \right)} = 0$$
Transform
$$\tan^{2}{\left(4 x \right)} + \tan{\left(4 x \right)} = 0$$
$$\left(\tan{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} = 0$$
Consider each factor separately
Step
$$\tan{\left(4 x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$\tan{\left(4 x \right)} = -1$$
This equation is transformed to
$$4 x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$4 x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
get the intermediate answer:
$$x = \frac{\pi n}{4} - \frac{\pi}{16}$$
Step
$$\tan{\left(4 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(4 x \right)} = 0$$
This equation is transformed to
$$4 x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$4 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
get the intermediate answer:
$$x = \frac{\pi n}{4} - \frac{\pi}{16}$$
$$x = \frac{\pi n}{4}$$
The final answer:
$$x_{1} = \frac{\pi n}{4} - \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{4}$$
Sum and product of roots
[src]
sum
-pi
0 + ----
16
$$\left(0\right) + \left(- \frac{\pi}{16}\right)$$
=
-pi ---- 16
$$- \frac{\pi}{16}$$
product
-pi
0 * ----
16
$$\left(0\right) * \left(- \frac{\pi}{16}\right)$$
=
0
$$0$$
Numerical answer
[src]
x1 = -67.7405915930299
x2 = -21.9911485751286
x3 = 87.9645943005142
x4 = -89.7317401681585
x5 = 33.7721210260903
x6 = 18.0641577581413
x7 = 64.2062998577414
x8 = 9.42477796076938
x9 = -42.4115008234622
x10 = -45.7494430179014
x11 = -3.92699081698724
x12 = 68.329640215578
x13 = 21.9911485751286
x14 = 72.2566310325652
x15 = 42.2151512826128
x16 = 95.8185759344887
x17 = -29.845130209103
x18 = -49.6764338348886
x19 = 80.1106126665397
x20 = 25.9181393921158
x21 = -15.707963267949
x22 = -73.8274273593601
x23 = -81.6814089933346
x24 = 86.1974484328699
x25 = -77.7544181763474
x26 = -23.7582944427728
x27 = 0.0
x28 = 98.174770424681
x29 = -7.85398163397448
x30 = 100.530964914873
x31 = 2.35619449019234
x32 = 73.8274273593601
x33 = -32.2013246992954
x34 = 6.28318530717959
x35 = 20.2240027074843
x36 = -37.6991118430775
x37 = 65.9734457253857
x38 = -18.0641577581413
x39 = -76.1836218495525
x40 = -14.1371669411541
x41 = -59.6902604182061
x42 = 54.1924732744239
x43 = 29.845130209103
x44 = 38.2881604656256
x45 = -65.9734457253857
x46 = -37.1100632205294
x47 = 14.1371669411541
x48 = -43.9822971502571
x49 = 24.3473430653209
x50 = -25.9181393921158
x51 = -98.174770424681
x52 = 7.85398163397448
x53 = 57.1377163871644
x54 = 79.1288649622929
x55 = -36.1283155162826
x56 = -47.9092879672443
x57 = 38.484510006475
x58 = -95.8185759344887
x59 = -27.6852852597601
x60 = -11.7809724509617
x61 = 76.1836218495525
x62 = -95.0331777710912
x63 = -69.9004365423729
x64 = 11.7809724509617
x65 = 36.1283155162826
x66 = -51.8362787842316
x67 = 94.2477796076938
x68 = 46.3384916404494
x69 = -80.1106126665397
x70 = 91.8915851175014
x71 = 28.2743338823081
x72 = -40.0553063332699
x73 = -5.6941366846315
x74 = -55.7632696012188
x75 = -58.1194640914112
x76 = 69.9004365423729
x77 = -91.8915851175014
x78 = -10.2101761241668
x79 = 16.2970118904971
x80 = 90.3207887907066
x81 = -1.76714586764426
x82 = -71.4712328691678
x83 = 60.2793090407542
x84 = 40.0553063332699
x85 = -33.7721210260903
x86 = -99.7455667514759
x87 = 3.92699081698724
x88 = -54.1924732744239
x89 = -87.9645943005142
x90 = -85.8047493511712
x91 = 43.9822971502571
x92 = 62.0464549083984
x93 = 58.1194640914112
x94 = 50.2654824574367
x95 = 51.8362787842316
x96 = 82.2704576158827
x97 = 47.9092879672443
x98 = -84.037603483527
x99 = 84.037603483527
x100 = -62.0464549083984
x100 = -62.0464549083984
The graph