What is the general equation of a sine function with an amplitude of 6, a period of pi/4, and a horizontal shift of pi/2? a. y = sin ( ( 8 ( x - pi/2 ) ) b. y = 8sin ( ( 4 ( x - pi/2 ) ) c. y= 6sin ( ( 8 ( x - pi/2 ) ) d. y = 6sin (8x) +pi/2

The formula for the period is and the formula for the phase shift is , the same b value as in the period.  The general form of the sin function is , where A is the amplitude. We are given the period as , so we will use the formula for the period to solve for b: .  Cross multiply to get and b = 8.  Now the phase shift.  We will use the formula for phase shift along with the b value we found to find c.  The phase shift (horizontal shift) is , so fitting that into our formula, .  Cross multiply to get and .  Now let's put all this together.  .  We will factor out the 8 to get the final equation of , choice C from above.