What Are the Characteristics of This Sine Curve Equation?

[silentthoughts]

Help me with sine questions.. URGENT

Hi I am trying to solve these and i can't understand them .. please help me

Q1:: Write an equation for a sine curve that has the following characteristics: - amplitude of 5, -max of 7, min of -3 and one cycle starts at pi/8 and this cycle ends at 9 pi/8



Q2:the number of hrs of daylight for a particular area is related to the day of the year as follows: D=12 +2.5 sin[2pi/365(t-81)], where D is the number of hours of daylight and t is the day of the year, with t= 1 representing january 1st. find the amplitude, period , phase shift and vertical shift for the equation.

 

[HallsofIvy]

Any "sin curve" can be written y= A sin(bx+ c)+ D. Since the largest possible value of sine is 1 and the smallest is -1, that will have a largest value of A+ D and smallest of -A+ D. One cycle of sin(x) starts at x= 0 and ends at x= 2$\pi$. One cycle of sin(bx+ c), then, starts when bx+ c= 0 and ends when bx+ c= 2$\pi$. Use the information given to find A, b, c, and D.