Advanced Functions Trig Problem

Question

A swimmer on a floating air mattress will follow the rise and fall of the waves in lake. When the person is on the top of the wave her feet are 0.5m above the average surface height of the lake. When she is in a trough her feet dig 0.5m into the water (-0.5m). The peaks of the waves are separated by two seconds. Create an equation of the sinusoidal function that models this movement assuming that she starts at the average surface height of the lake and heads upwards.

Answer 1

y = Asin(Bx)

A = amplitude = 0.5

Period = 2π/B = 2

2π = 2B

So, B = π

y = 0.5sin(πx)

Answer 2

Wave height= 5+5=a.

Length=2sec*speed=b.

a^2+b^2=c^2 (hypotenuse)