Mister Exam

Other calculators

tan(-22.3°)=2*tan(x°) equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
   //-223*pi\\              
   ||-------||              
   |\   10  /|        /x*pi\
tan|---------| = 2*tan|----|
   \   360   /        \360 /
tan⁡((−1)22310π360)=2tan⁡(πx360)\tan{\left(\frac{\left(-1\right) \frac{223}{10} \pi}{360} \right)} = 2 \tan{\left(\frac{\pi x}{360} \right)}
Simplify
Detail solution
Given the equation
tan⁡((−1)22310π360)=2tan⁡(πx360)\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⁡(πx360)=−tan⁡(223π3600)2\tan{\left(\frac{\pi x}{360} \right)} = - \frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2}
This equation is transformed to
πx360=πn+atan⁡(−tan⁡(223π3600)2)\frac{\pi x}{360} = \pi n + \operatorname{atan}{\left(- \frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}
Or
πx360=πn−atan⁡(tan⁡(223π3600)2)\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
π360\frac{\pi}{360}
we get the answer:
x1=360(πn−atan⁡(tan⁡(223π3600)2))πx_{1} = \frac{360 \left(\pi n - \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}\right)}{\pi}
The graph
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
              /   /223*pi\\
              |tan|------||
              |   \ 3600 /|
     -360*atan|-----------|
              \     2     /
x1 = ----------------------
               pi
x1=−360atan⁡(tan⁡(223π3600)2)πx_{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
−360atan⁡(tan⁡(223π3600)2)π- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi} 
=
         /   /223*pi\\
         |tan|------||
         |   \ 3600 /|
-360*atan|-----------|
         \     2     /
----------------------
          pi
−360atan⁡(tan⁡(223π3600)2)π- \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
−360atan⁡(tan⁡(223π3600)2)π- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi} 
=
         /   /223*pi\\
         |tan|------||
         |   \ 3600 /|
-360*atan|-----------|
         \     2     /
----------------------
          pi
−360atan⁡(tan⁡(223π3600)2)π- \frac{360 \operatorname{atan}{\left(\frac{\tan{\left(\frac{223 \pi}{3600} \right)}}{2} \right)}}{\pi} 
-360*atan(tan(223*pi/3600)/2)/pi
Numerical answer [src] 
x1 = -11.2565712594489
x1 = -11.2565712594489
    © Mister Exam – Calculator