Mister Exam
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Equation 5x^2-8x+3=0
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Equation x-2=-3x
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Identical expressions
- tan(- twenty-two . three °)= two *tan(x°)
- tangent of ( minus 22.3°) equally 2 multiply by tangent of (x°)
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- tan(-22.3°)=2tan(x°)
- tan-22.3°=2tanx°
-
Similar expressions
- tan(22.3°)=2*tan(x°)
tan(-22.3°)=2*tan(x°) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
//-223*pi\\ ||-------|| |\ 10 /| /x*pi\ tan|---------| = 2*tan|----| \ 360 / \360 /
$$\tan{\left(\frac{\left(-1\right) \frac{223}{10} \pi}{360} \right)} = 2 \tan{\left(\frac{\pi x}{360} \right)}$$
Detail solution
Given the equation
$$\tan{\left(\frac{\left(-1\right) \frac{223}{10} \pi}{360} \right)} = 2 \tan{\left(\frac{\pi x}{360} \right)}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(\frac{\pi x}{360} \right)} = - \frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2}$$
This equation is transformed to
$$\frac{\pi x}{360} = \pi n + \operatorname{atan}{\left(- \frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}$$
Or
$$\frac{\pi x}{360} = \pi n - \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{360}$$
we get the answer:
$$x_{1} = \frac{360 \left(\pi n - \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}\right)}{\pi}$$
$$\tan{\left(\frac{\left(-1\right) \frac{223}{10} \pi}{360} \right)} = 2 \tan{\left(\frac{\pi x}{360} \right)}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -2
The equation is transformed to
$$\tan{\left(\frac{\pi x}{360} \right)} = - \frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2}$$
This equation is transformed to
$$\frac{\pi x}{360} = \pi n + \operatorname{atan}{\left(- \frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}$$
Or
$$\frac{\pi x}{360} = \pi n - \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{360}$$
we get the answer:
$$x_{1} = \frac{360 \left(\pi n - \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}\right)}{\pi}$$
Rapid solution
[src]
/ /223*pi\\
|tan|------||
| \ 3600 /|
-360*atan|-----------|
\ 2 /
x1 = ----------------------
pi
$$x_{1} = - \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi}$$
x1 = -360*atan(tan(223*pi/3600)/2)/pi
Sum and product of roots
[src]
sum
/ /223*pi\\
|tan|------||
| \ 3600 /|
-360*atan|-----------|
\ 2 /
----------------------
pi
$$- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi}$$
=
/ /223*pi\\
|tan|------||
| \ 3600 /|
-360*atan|-----------|
\ 2 /
----------------------
pi
$$- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi}$$
product
/ /223*pi\\
|tan|------||
| \ 3600 /|
-360*atan|-----------|
\ 2 /
----------------------
pi
$$- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi}$$
=
/ /223*pi\\
|tan|------||
| \ 3600 /|
-360*atan|-----------|
\ 2 /
----------------------
pi
$$- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi}$$
-360*atan(tan(223*pi/3600)/2)/pi