Mister Exam
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How to use it?
- Equation:
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Equation tg²x-5tgx-6=0
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Equation √3+tg(x/6)=0
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Equation tan(x)=-1
-
Equation 6^x+8^x=10^x
- Express {x} in terms of y where:
- -12*x+3*y=-9
- -18*x-1*y=-11
- 17*x-15*y=-17
- 2*x-15*y=-1
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Identical expressions
- √ three +tg(x/ six)= zero
- √3 plus tg(x divide by 6) equally 0
- √ three plus tg(x divide by six) equally zero
- √3+tgx/6=0
- √3+tg(x/6)=O
- √3+tg(x divide by 6)=0
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Similar expressions
- √3-tg(x/6)=0
√3+tg(x/6)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
___ /x\
\/ 3 + tan|-| = 0
\6/
$$\tan{\left(\frac{x}{6} \right)} + \sqrt{3} = 0$$
Detail solution
Given the equation
$$\tan{\left(\frac{x}{6} \right)} + \sqrt{3} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(\frac{x}{6} \right)} = - \sqrt{3}$$
This equation is transformed to
$$\frac{x}{6} = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Or
$$\frac{x}{6} = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{6}$$
we get the answer:
$$x_{1} = 6 \pi n - 2 \pi$$
$$\tan{\left(\frac{x}{6} \right)} + \sqrt{3} = 0$$
- this is the simplest trigonometric equation
Move sqrt(3) to right part of the equation
with the change of sign in sqrt(3)
We get:
$$\tan{\left(\frac{x}{6} \right)} = - \sqrt{3}$$
This equation is transformed to
$$\frac{x}{6} = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Or
$$\frac{x}{6} = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{6}$$
we get the answer:
$$x_{1} = 6 \pi n - 2 \pi$$
Sum and product of roots
[src]
sum
-2*pi
$$\left(- 2 \pi\right)$$
=
-2*pi
$$- 2 \pi$$
product
-2*pi
$$\left(- 2 \pi\right)$$
=
-2*pi
$$- 2 \pi$$
Numerical answer
[src]
x1 = -25.1327412287183
x2 = -62.8318530717959
x3 = 87.9645943005142
x4 = -81.6814089933346
x5 = 69.1150383789755
x6 = -100.530964914873
x7 = -43.9822971502571
x8 = 12.5663706143592
x9 = -6.28318530717959
x10 = 31.4159265358979
x11 = 50.2654824574367
x11 = 50.2654824574367
The graph