At a dock on the east coast, low tide occurs at 3 p. m. with a water depth of 5 ft. The depth at high tide is 83 ft. High tide occurs every 6 hours. Explain how to find the sinusoidal function that models the depth in terms of time, x.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116