Question

Pleasee help me. How do I plug in 14meters into this equation to find the time?

Answer 1

D = depth

D(t) = 5sin30(t-5) + 16.
The depth is 14...I'm supposed to find time. (t).

Answer 2

? ~

Answer 3

So you're solving
14=5sin(30(t-5)) + 16?

Answer 4

yep

Answer 5

What if we transpose 16 to the other side and continue from:
5sin(30(t-5)) = -2

Answer 6

true

Answer 7

What do you get for solution of
sin(30(t-5))=-2/5

Answer 8

not sure dont I need t?

Answer 9

Solve first for the general solution for
sin(30(t-5))=-2/5
then t can be solved from the general solution algebraically.

Answer 10

thanks for your help......but what do you mean by general solution?

Answer 11

sin is a periodic function, so
sin(x)=1/2 has a solution of pi/6, or 5pi/6, or pi/6+2pi, ...
The general solution is therefore
pi/6+2k(pi) or 5pi/6+2k(pi).
where k is an integer.
Since the question does not specify the limits of t, the solution should be derived from the general solution.
I hope I made my point clear.

Answer 12

Probably, but that's not the way we've learnt it . Thanks anyways

Answer 13

You're welcome!

Answer 14

If you accept a solution within a range, then solve for sin(x)=-2/5 (approx. 2.73 for 0<x<pi).
since
30(t-5)=2.73 (assuming you are working with radians)
you can solve for t (for 0<x<2pi)

Answer 15

\[t=\frac{1}{30} \left(150-\sin ^{-1}\left(\frac{2}{5}\right)\right) \]A detailed solution is attached.