Question

The wave passes through the following coordinates: left parenthesis negative pi comma 0.6 right parenthesis, left parenthesis Start Fraction negative pi over 4 End Fraction comma negative 1 right parenthesis, left parenthesis Start Fraction 3 pi over 4 End Fraction comma 1 right parenthesis, and left parenthesis Start Fraction 5 pi over 2 End Fraction comma negative 1 right parenthesis.

Determine the equation of the sine function shown in the graph.

(1 point)

f(x)=sinx+π4


f(x)=sin(x−π4)


f(x)=sinx−π4


f(x)=sin(x+π4)

Answer 1

f(x) = sin(x − π/4)

Reason: amplitude = 1 and period = 2π, and the minimum at x = −π/4 means x − φ = −π/2 so φ = π/4, giving f(x) = sin(x − π/4).