Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation e^x=0
-
Equation 10*(x-9)=7
-
Equation cos(x)=3
-
Equation 3-3*6+2=x
- Express {x} in terms of y where:
- -11*x+10*y=-9
- -9*x-15*y=-4
- 1*x+5*y=-11
- -11*x-15*y=14
-
Identical expressions
- tg(pi(x+ ten)/ three)=-√ three / three
- tg( Pi (x plus 10) divide by 3) equally minus √3 divide by 3
- tg( Pi (x plus ten) divide by three) equally minus √ three divide by three
- tgpix+10/3=-√3/3
- tg(pi(x+10) divide by 3)=-√3 divide by 3
-
Similar expressions
- (tg(pi*(x+10)/3))=-√3/3
- tg(pi(x+10)/3)=+√3/3
- tg(pi(x-10)/3)=-√3/3
tg(pi(x+10)/3)=-√3/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /pi*(x + 10)\ -\/ 3 tan|-----------| = ------- \ 3 / 3
$$\tan{\left(\frac{\pi \left(x + 10\right)}{3} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(\frac{\pi \left(x + 10\right)}{3} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{3} + \frac{\pi}{3} = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{\pi x}{3} + \frac{\pi}{3} = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{3} = \pi n - \frac{\pi}{2}$$
Divide both parts of the equation by
$$\frac{\pi}{3}$$
we get the answer:
$$x_{1} = \frac{3 \left(\pi n - \frac{\pi}{2}\right)}{\pi}$$
$$\tan{\left(\frac{\pi \left(x + 10\right)}{3} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{3} + \frac{\pi}{3} = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{\pi x}{3} + \frac{\pi}{3} = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{3} = \pi n - \frac{\pi}{2}$$
Divide both parts of the equation by
$$\frac{\pi}{3}$$
we get the answer:
$$x_{1} = \frac{3 \left(\pi n - \frac{\pi}{2}\right)}{\pi}$$
Sum and product of roots
[src]
sum
-3/2
$$- \frac{3}{2}$$
=
-3/2
$$- \frac{3}{2}$$
product
-3/2
$$- \frac{3}{2}$$
=
-3/2
$$- \frac{3}{2}$$
-3/2
Numerical answer
[src]
x1 = 1.5
x2 = 82.5
x3 = -16.5
x4 = 34.5
x5 = -58.5
x6 = -13.5
x7 = -37.5
x8 = 64.5
x9 = -28.5
x10 = -85.5
x11 = -67.5
x12 = -34.5
x13 = 79.5
x14 = 10.5
x15 = 94.5
x16 = -64.5
x17 = -31.5
x18 = -88.5
x19 = 46.5
x20 = 25.5
x21 = -40.5
x22 = 55.5
x23 = 76.5
x24 = 40.5
x25 = 13.5
x26 = -46.5
x27 = -91.5
x28 = 7.5
x29 = -61.5
x30 = -43.5
x31 = 85.5
x32 = -94.5
x33 = -10.5
x34 = 4.5
x35 = -25.5
x36 = 22.5
x37 = 67.5
x38 = 31.5
x39 = 100.5
x40 = 97.5
x41 = -79.5
x42 = 43.5
x43 = 16.5
x44 = 19.5
x45 = -97.5
x46 = -73.5
x47 = -52.5
x48 = -49.5
x49 = 73.5
x50 = -55.5
x51 = -76.5
x52 = 49.5
x53 = 37.5
x54 = 70.5
x55 = -7.5
x56 = -1.5
x57 = 88.5
x58 = -22.5
x59 = 91.5
x60 = 61.5
x61 = -70.5
x62 = 58.5
x63 = -4.5
x64 = -82.5
x65 = -100.5
x66 = 28.5
x67 = 52.5
x68 = -19.5
x68 = -19.5