What is the general equation of a sine function with an amplitude of 6 , a period of pi over 4 , and a horizontal shift of pi over 2 ?
Answer
A
y is equal to sine of open paren 8 times open paren x minus pi over 2 close paren close paren
B
y is equal to 6 sine open paren 8 times open paren x minus pi over 2 close paren close paren
C
y is equal to 6 sine 8 x plus pi over 2
D
y is equal to 8 sine open paren 4 times open paren x minus pi over 2 close paren close paren
Explanation
A sine function with amplitude 6 has a coefficient of 6 in front of sine. Its period is 2π divided by the coefficient of x, so 2π/B = π/4 gives B = 8. A horizontal shift of π/2 to the right is written as (x − π/2), so the equation is y = 6 sin(8(x − π/2)), choice B.
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