Mister Exam

Other calculators

sin(pi(x+4)/6)=-0.5 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] 
   /pi*(x + 4)\       
sin|----------| = -1/2
   \    6     /
sin⁡(π(x+4)6)=−12\sin{\left(\frac{\pi \left(x + 4\right)}{6} \right)} = - \frac{1}{2}
Simplify
Detail solution
Given the equation
sin⁡(π(x+4)6)=−12\sin{\left(\frac{\pi \left(x + 4\right)}{6} \right)} = - \frac{1}{2}
- this is the simplest trigonometric equation
This equation is transformed to
πx6+π6=πn+acos⁡(−12)\frac{\pi x}{6} + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}
πx6+π6=πn−π+acos⁡(−12)\frac{\pi x}{6} + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}
Or
πx6+π6=πn+2π3\frac{\pi x}{6} + \frac{\pi}{6} = \pi n + \frac{2 \pi}{3}
πx6+π6=πn−π3\frac{\pi x}{6} + \frac{\pi}{6} = \pi n - \frac{\pi}{3}
, where n - is a integer
Move
π6\frac{\pi}{6}
to right part of the equation
with the opposite sign, in total:
πx6=πn+π2\frac{\pi x}{6} = \pi n + \frac{\pi}{2}
πx6=πn−π2\frac{\pi x}{6} = \pi n - \frac{\pi}{2}
Divide both parts of the equation by
π6\frac{\pi}{6}
we get the answer:
x1=6(πn+π2)πx_{1} = \frac{6 \left(\pi n + \frac{\pi}{2}\right)}{\pi}
x2=6(πn−π2)πx_{2} = \frac{6 \left(\pi n - \frac{\pi}{2}\right)}{\pi}
The graph
0-80-60-40-2020406080-1001002-2
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 3
x1=3x_{1} = 3 
x2 = 7
x2=7x_{2} = 7 
x2 = 7
Sum and product of roots [src] 
sum
3 + 7
3+73 + 7 
=
10
1010 
product
3*7
3⋅73 \cdot 7 
=
21
2121 
21
Numerical answer [src] 
x1 = -5.0
x2 = -21.0
x3 = 63.0
x4 = 67.0
x5 = -81.0
x6 = 3.0
x7 = 39.0
x8 = 15.0
x9 = 27.0
x10 = -53.0
x11 = 51.0
x12 = -89.0
x13 = -17.0
x14 = 19.0
x15 = -93.0
x16 = -101.0
x17 = -105.0
x18 = 31.0
x19 = -65.0
x20 = 55.0
x21 = -9.0
x22 = -69.0
x23 = 87.0
x24 = -29.0
x25 = 79.0
x26 = -33.0
x27 = 99.0
x28 = 7.0
x29 = -77.0
x30 = -57.0
x31 = -45.0
x32 = 43.0
x33 = 91.0
x34 = -41.0
x35 = 75.0
x35 = 75.0
    © Mister Exam – Calculator