The values of a and b are 2 and π/5, respectively
How to determine the values of a and b?
The graph of the complete question is added as an attachment
The equation of the graph is given as:
y = sin(ax - b)
From the graph, we have the following points:
(π/10, 0), (3π/5, 0) and (11π/10, 0)
Substitute the above points in y = sin(ax - b)
sin(a(π/10) - b) = 0 and sin(a(3π/5) - b) = 0
Take the arc sin of both sides
a(π/10) - b = 0
a(3π/5) - b = π
Subtract the equations to eliminate b
a(π/10) - a(3π/5) = -π
Divide through by π
a(1/10) - a(3/5) = -1
Express fractions as decimals
0.1a - 0.6a = -1
Evaluate the difference
-0.5a = -1
Divide by -0.5
a = 2
Substitute a = 2 in a(3π/5) - b = π
2 * (3π/5) - b = π
Evaluate the product
6π/5 - b = π
This gives
b = 6π/5 - π
Evaluate the difference
b = π/5
Hence, the values of a and b are 2 and π/5, respectively
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