The general equation of a sine curve is [tex]y = A(\sin(B(x+c)) + D[/tex]
The values of a and b for [tex]y = \sin(ax - b)[/tex] are: 2 and [tex]\frac{\pi}{5}[/tex]
Given that
[tex]y = \sin(ax - b)[/tex]
[tex]a > 0, 0 < b < \pi[/tex]
And the points are:
[tex](x,y) = \{(\frac{\pi}{10},0),(\frac{3\pi}{5},0),(\frac{11\pi}{10},0)\}[/tex]
The period (T) of the function is calculated as follows:
[tex]T = \frac{2\pi}{a}[/tex]
[tex]a > 0, 0 < b < \pi[/tex] implies that, the period (T) is:
[tex]T = \pi[/tex]
So, we have:
[tex]\frac{2\pi}{a} = \pi[/tex]
Solve for a
[tex]a = \frac{2\pi}{\pi}[/tex]
[tex]a = 2[/tex]
So, we have:
[tex]y = \sin(ax - b)[/tex]
[tex]y = \sin(2x - b)[/tex]
Using one of the given points [tex](\frac{\pi}{10},0)[/tex]
The equation becomes
[tex]0 = \sin(2 \times \frac{\pi}{10} - b)[/tex]
[tex]0 = \sin(\frac{\pi}{5} - b)[/tex]
Take arc sin of both sides
[tex]\sin^{-1}(0) = \frac{\pi}{5} - b[/tex]
[tex]0 = \frac{\pi}{5} - b[/tex]
Collect like terms
[tex]b = \frac{\pi}{5}[/tex]
Hence, the values of a and b are: 2 and [tex]\frac{\pi}{5}[/tex]
Read more about sine curves at:
https://brainly.com/question/4769300
