Question

the height 'h' meters of water in a harbour 't' hours after noon is depicted by:
h = 4+2sin(30t)
a boat can enter the harbour if the water is atleast 3 meters high. Find the times before midnight which the boat CAN'T enter the harbour.

Answer 1

now the minimum is 2, and the maximum is 6.

Answer 2

and if it can't be in the harbour, it must be
4 + 2sin(30t) < 3
is this right??

Answer 3

then i get
sin(30t) < -0.5

Answer 4

but now how do I solve it??

Answer 5

u want to know hoe to solve sin^-1 (-0.5) ?

Answer 6

what is sin^-1(0.5) = ?

Answer 7

After noon and before midnight means t goes from 0 to 12

Answer 8

It would be good first to find values of t for which sin(30t) = -0.5

Answer 9

7, 11 :P

Answer 10

So, if t is from 0 to 7, is sin(30t) < -0.5 ?

Answer 11

no.

Answer 12

Then, from 0 to 7, the boat can't enter. How about from 7 to 11?

Answer 13

ohhh, ok, got it. so 7<t<11

Answer 14

:)

Answer 15

lol thanks :)