Mister Exam

Other calculators

sin(x/4-pi/8)=0 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   pi\    
sin|- - --| = 0
   \4   8 /
sin⁡(x4−π8)=0\sin{\left(\frac{x}{4} - \frac{\pi}{8} \right)} = 0
Simplify
Detail solution
Given the equation
sin⁡(x4−π8)=0\sin{\left(\frac{x}{4} - \frac{\pi}{8} \right)} = 0
- this is the simplest trigonometric equation
with the change of sign in 0

We get:
sin⁡(x4−π8)=0\sin{\left(\frac{x}{4} - \frac{\pi}{8} \right)} = 0
Divide both parts of the equation by -1

The equation is transformed to
cos⁡(x4+3π8)=0\cos{\left(\frac{x}{4} + \frac{3 \pi}{8} \right)} = 0
This equation is transformed to
x4+3π8=πn+acos⁡(0)\frac{x}{4} + \frac{3 \pi}{8} = \pi n + \operatorname{acos}{\left(0 \right)}
x4+3π8=πn−π+acos⁡(0)\frac{x}{4} + \frac{3 \pi}{8} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}
Or
x4+3π8=πn+π2\frac{x}{4} + \frac{3 \pi}{8} = \pi n + \frac{\pi}{2}
x4+3π8=πn−π2\frac{x}{4} + \frac{3 \pi}{8} = \pi n - \frac{\pi}{2}
, where n - is a integer
Move
3π8\frac{3 \pi}{8}
to right part of the equation
with the opposite sign, in total:
x4=πn+π8\frac{x}{4} = \pi n + \frac{\pi}{8}
x4=πn−7π8\frac{x}{4} = \pi n - \frac{7 \pi}{8}
Divide both parts of the equation by
14\frac{1}{4}
we get the answer:
x1=4πn+π2x_{1} = 4 \pi n + \frac{\pi}{2}
x2=4πn−7π2x_{2} = 4 \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} 
     9*pi
x2 = ----
      2
x2=9π2x_{2} = \frac{9 \pi}{2} 
x2 = 9*pi/2
Sum and product of roots [src] 
sum
pi   9*pi
-- + ----
2     2
π2+9π2\frac{\pi}{2} + \frac{9 \pi}{2} 
=
5*pi
5π5 \pi 
product
pi 9*pi
--*----
2   2
π29π2\frac{\pi}{2} \frac{9 \pi}{2} 
=
    2
9*pi 
-----
  4
9π24\frac{9 \pi^{2}}{4} 
9*pi^2/4
Numerical answer [src] 
x1 = 39.2699081698724
x2 = 103586.163770489
x3 = -86.3937979737193
x4 = -98.9601685880785
x5 = -174.358392274234
x6 = 14.1371669411541
x7 = -48.6946861306418
x8 = 139.800873084746
x9 = -589.048622548086
x10 = 1.5707963267949
x11 = -450.818545790135
x12 = 51.8362787842316
x13 = -10.9955742875643
x14 = 26.7035375555132
x15 = -23.5619449019235
x16 = 190.066355542182
x17 = 102.101761241668
x18 = 76.9690200129499
x19 = -36.1283155162826
x20 = -73.8274273593601
x21 = 64.4026493985908
x22 = 89.5353906273091
x23 = -61.261056745001
x23 = -61.261056745001
    © Mister Exam – Calculator