Mister Exam

Other calculators

sin(x/3)=-1/2

sin(x/3)=-1/2 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] 
   /x\       
sin|-| = -1/2
   \3/
sin⁡(x3)=−12\sin{\left(\frac{x}{3} \right)} = - \frac{1}{2}
Simplify
Detail solution
Given the equation
sin⁡(x3)=−12\sin{\left(\frac{x}{3} \right)} = - \frac{1}{2}
- this is the simplest trigonometric equation
This equation is transformed to
x3=2πn+asin⁡(−12)\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}
x3=2πn−asin⁡(−12)+π\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi
Or
x3=2πn−π6\frac{x}{3} = 2 \pi n - \frac{\pi}{6}
x3=2πn+7π6\frac{x}{3} = 2 \pi n + \frac{7 \pi}{6}
, where n - is a integer
Divide both parts of the equation by
13\frac{1}{3}
we get the answer:
x1=6πn−π2x_{1} = 6 \pi n - \frac{\pi}{2}
x2=6πn+7π2x_{2} = 6 \pi n + \frac{7 \pi}{2}
The graph
0-80-60-40-2020406080-1001002-2
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     -pi 
x1 = ----
      2
x1=−π2x_{1} = - \frac{\pi}{2} 
     7*pi
x2 = ----
      2
x2=7π2x_{2} = \frac{7 \pi}{2} 
x2 = 7*pi/2
Sum and product of roots [src] 
sum
  pi   7*pi
- -- + ----
  2     2
−π2+7π2- \frac{\pi}{2} + \frac{7 \pi}{2} 
=
3*pi
3π3 \pi 
product
-pi  7*pi
----*----
 2    2
−π27π2- \frac{\pi}{2} \frac{7 \pi}{2} 
=
     2
-7*pi 
------
  4
−7π24- \frac{7 \pi^{2}}{4} 
-7*pi^2/4
Numerical answer [src] 
x1 = -76.9690200129499
x2 = -359.712358836031
x3 = 86.3937979737193
x4 = -39.2699081698724
x5 = -58.1194640914112
x6 = -83.2522053201295
x7 = 92.6769832808989
x8 = -20.4203522483337
x9 = -102.101761241668
x10 = 67.5442420521806
x11 = -26.7035375555132
x12 = -64.4026493985908
x13 = -1.5707963267949
x14 = 17.2787595947439
x15 = -95.8185759344887
x16 = 10.9955742875643
x17 = 36.1283155162826
x18 = 48.6946861306418
x19 = 111.526539202438
x20 = -7.85398163397448
x21 = 73.8274273593601
x22 = 29.845130209103
x23 = -45.553093477052
x24 = 54.9778714378214
x24 = 54.9778714378214
The graph
sin(x/3)=-1/2 equation
    © Mister Exam – Calculator