Question

The formula H(t)=3.2+2sin(0.5t) models the height of the tide at a beach where t represents the number of hours after midnight.

a)For what values of t between 0 and 6 would the tide be exactly 5 feet high? Set up and solve an appropriate equation and use two-decimal accuracy for answers.

Answer 1

5 = 3.2 + 2sin(0.5t)
sin(0.5t) = (5 - 3.2)/ 2 = 0.9

now you need to find values whose sine is 0.9

Answer 2

set your calculator to radians

Answer 3

inverse sine of 0.9?

Answer 4

yes

Answer 5

the lowest is 1.12 correct to 2 dec places

Answer 6

that's not the answer though is it? when graphed, the point on the wave closest to five appears to have to be in between 2 and 3

Answer 7

oh ok
lets look at that again...

Answer 8

oops sorry 0.5t = 1.12

Answer 9

silly me..

Answer 10

so t = 2.24?

Answer 11

right

Answer 12

checks out with the graph. thank you so much!

Answer 13

yw

Answer 14

oh theres another value between 0 and 6
can you figure out what it is?

Answer 15

the sine is also positive in the 2nd quadrant so the other possible value for 0.5t is pi - 1.12
or 2.02

so other values of t = 4.04

Answer 16

can you see that on the graph?