Functions 11 - Trigonometry Problem

Question

The displacement of a raft in metres in the water is described by the function b(t) = 4sin(18t) at time ‘t’ seconds. If the raft starts at the center, when is the second time that the raft will be back at the center?

Answer 1

Hi Ayaan!

It may be helpful to think about the sine wave that this function is describing. The problem states that the raft starts in the center, meaning at t=0, the raft will be in the center, and the displacement b(t) will also be 0 (you can check this by solving for b(0)). So, if the question is when will the raft return to the center next, we just want to solve for the value of t closest to 0 where b(t)=0. This now gives us an idea of what to do algebraically to solve the problem:

1) b(t)=4sin(18t)=0

2) sin(18t)=0

3)18t=0,pi/2,pi...

4) t=pi/36

One step that you may get confused at is how to get to step 3. Don't get scared by the 18t, this problem is the same as asking when does sin(x) equal 0, and you can refer back to your unit circle to figure out the specific radian values.

Hope this helps!