Question

The wave crest is at y equals 1 and the trough is at y equals negative 1. The wave passes through the following coordinates: left parenthesis negative 2 pi comma negative 1 right parenthesis, left parenthesis negative pi comma 1 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, left parenthesis start fraction pi over 2 end fraction comma 0 right parenthesis, left parenthesis pi comma 1 right parenthesis, left parenthesis start fraction 3 pi over 2 end fraction comma 0 right parenthesis, and left parenthesis 2 pi comma negative 1 right parenthesis.

Which of the following functions correctly represents the graph of the sine function given in the preceding image?

(1 point)

f(x)=sin(x+π2)


f(x)=sin(x−π)


f(x)=sin(x−π2)


f(x)=sin(x−π4)

Answer 1

f(x) = sin(x − π/2)

Reason: sin(x − π/2) gives sin(π/2 − π/2)=0 at x = π/2, sin(0 − π/2)= −1 at x = 0, sin(−π − π/2)=sin(−3π/2)=1 at x = −π, and sin(2π − π/2)=sin(3π/2)= −1 at x = 2π, matching the given points.