Find a function of the form y Asin kz C or y Acos kz C w

Find a function of the form y = Asin (kz) + C or y = Acos (kz) + C whose graph matches the function shown below: 7 6 Leave your answer in exact form; if necessary, type pi for . Preview Get help: Video

Solution

1) Let cos = cos(cos^-1(r/5))

cos = r/5

Now using cos = Base/hyp = r/5

Then opp = sqrt[hyp^2 – base^2] = sqrt(25 – r²)

Then sin = sin(cos^-1(r/5)) = sqrt(25 – r²)/r

2) Let sin = sin(sin^-1(y/9))

sin = y/9

Now using sin = opp/hyp = y/9

Then Base = sqrt[hyp^2 – opp^2] = sqrt(81 – y²)

Then tan = tan(sin^-1(y/9)) = y/sqrt(81 – y²)

3) Let sin = sin(sin^-1(1/11))

sin = 1/11

Now using sin = opp/hyp = 1/11

Then Base = sqrt[hyp^2 – opp^2] = sqrt(120)

Then cos = cos(sin^-1(1/11)) = sqrt(120)/11