Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation e^x=0
-
Equation x^2+2x-3=0
-
Equation x^2-3*x+3=0
-
Equation √(x^2-1)^3=2*x
- Express {x} in terms of y where:
- 2*x+2*y=-6
- -9*x-4*y=-20
- 12*x-13*y=-14
- 1*x+5*y=-11
- Sum of series:
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-1
- Derivative of:
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-1
- Integral of d{x}:
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-1
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Identical expressions
- tan(x/ three +pi/ six)=- one
- tangent of (x divide by 3 plus Pi divide by 6) equally minus 1
- tangent of (x divide by three plus Pi divide by six) equally minus one
- tanx/3+pi/6=-1
- tan(x divide by 3+pi divide by 6)=-1
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Similar expressions
- tan(x/3+pi/6)=+1
- tan(x/3-pi/6)=-1
tan(x/3+pi/6)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x pi\ tan|- + --| = -1 \3 6 /
$$\tan{\left(\frac{x}{3} + \frac{\pi}{6} \right)} = -1$$
Detail solution
Given the equation
$$\tan{\left(\frac{x}{3} + \frac{\pi}{6} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$\frac{x}{3} + \frac{\pi}{6} = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{x}{3} = \pi n - \frac{5 \pi}{12}$$
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n - \frac{5 \pi}{4}$$
$$\tan{\left(\frac{x}{3} + \frac{\pi}{6} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$\frac{x}{3} + \frac{\pi}{6} = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{x}{3} = \pi n - \frac{5 \pi}{12}$$
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n - \frac{5 \pi}{4}$$
Sum and product of roots
[src]
sum
-5*pi ----- 4
$$- \frac{5 \pi}{4}$$
=
-5*pi ----- 4
$$- \frac{5 \pi}{4}$$
product
-5*pi ----- 4
$$- \frac{5 \pi}{4}$$
=
-5*pi ----- 4
$$- \frac{5 \pi}{4}$$
-5*pi/4
Numerical answer
[src]
x1 = -60.4756585816035
x2 = 52.621676947629
x3 = 90.3207887907066
x4 = -79.3252145031423
x5 = 43.1968989868597
x6 = -88.7499924639117
x7 = -98.174770424681
x8 = -41.6261026600648
x9 = 14.9225651045515
x10 = -3.92699081698724
x11 = -51.0508806208341
x12 = -69.9004365423729
x13 = -13.3517687777566
x14 = -32.2013246992954
x15 = 24.3473430653209
x16 = 80.8960108299372
x17 = -22.776546738526
x18 = 71.4712328691678
x19 = 62.0464549083984
x20 = 99.7455667514759
x21 = 5.49778714378214
x22 = 33.7721210260903
x22 = 33.7721210260903