Mister Exam
Tgx-3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(x \right)} - 3 = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(x \right)} = 3$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
$$\tan{\left(x \right)} - 3 = 0$$
- this is the simplest trigonometric equation
Move -3 to right part of the equation
with the change of sign in -3
We get:
$$\tan{\left(x \right)} = 3$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
atan(3)
$$\operatorname{atan}{\left(3 \right)}$$
=
atan(3)
$$\operatorname{atan}{\left(3 \right)}$$
product
atan(3)
$$\operatorname{atan}{\left(3 \right)}$$
=
atan(3)
$$\operatorname{atan}{\left(3 \right)}$$
atan(3)
Numerical answer
[src]
x1 = 95.496825380092
x2 = -36.4500660706793
x3 = 7.53223107957784
x4 = -89.8571411817058
x5 = -136.981030985553
x6 = -45.8748440314486
x7 = -67.8659926065772
x8 = 42.0897502690656
x9 = 13.8154163867574
x10 = -99.2819191424751
x11 = 64.0808988441941
x12 = -80.4323632209364
x13 = 70.3640841513737
x14 = -96.1403264888853
x15 = -14.4589174955507
x16 = -52.1580293386282
x17 = -61.5828072993976
x18 = 92.3552327265023
x19 = -30.1668807634997
x20 = -39.5916587242691
x21 = -23.8836954563201
x22 = -83.5739558745262
x23 = -1.89254688119154
x24 = -17.6005101491405
x25 = 35.806564961886
x26 = 4.39063842598805
x27 = 86.0720474193227
x28 = 26.3817870011166
x29 = 20.098601693937
x30 = 48.3729355762452
x31 = 38.9481576154758
x32 = -8.17573218837112
x33 = -74.1491779137568
x33 = -74.1491779137568