Question

Rewrite the sine function f(x)=2sin(x+π2)−1
as a cosine function.(1 point)
Responses

f(x)=2cos(x−π2)−1

f left parenthesis x right parenthesis equals 2 cosine left parenthesis x minus Start Fraction pi over 2 End Fraction right parenthesis minus 1

f(x)=2cos(x+π4)−1

f left parenthesis x right parenthesis equals 2 cosine left parenthesis x plus Start Fraction pi over 4 End Fraction right parenthesis minus 1

f(x)=2cos(x+π)−1

f left parenthesis x right parenthesis equals 2 cosine left parenthesis x plus pi right parenthesis minus 1

f(x)=2cos(x)−1

f left parenthesis x right parenthesis equals 2 cosine left parenthesis x right parenthesis minus 1

Answer 1

Use the identity sin(θ + π/2) = cos θ. So

f(x) = 2 sin(x + π/2) − 1 = 2 cos x − 1.

Thus the correct choice is f(x) = 2 cos(x) − 1.