# Thread: Sin Graph - x coordinates help

1. ## Sin Graph - x coordinates help

Hi,

I'm working on my application task exercises for Trigonometric graphs, but I can't seem to work this sum out, A step by step explanation would be great:

The depth,
$\displaystyle D(t)$ metres, of water at the entrance to a harbour at t hours after midnight on a particular day is given by $\displaystyle D(t) = 10 + 3 sin (\frac{\pi t}{6}), 0 \leq t \leq 24$

1. Find the value of $\displaystyle t$ for which $\displaystyle D(t) \geq 8.5$

Any help would be greatly appreciated,

Thanks,

Dru

2. Originally Posted by 22upon7
Hi,

I'm working on my application task exercises for Trigonometric graphs, but I can't seem to work this sum out, A step by step explanation would be great:

The depth, $\displaystyle D(t)$ metres, of water at the entrance to a harbour at t hours after midnight on a particular day is given by $\displaystyle D(t) = 10 + 3 sin (\frac{\pi t}{6}), 0 \leq t \leq 24$

1. Find the value of $\displaystyle t$ for which $\displaystyle D(t) \geq 8.5$

Any help would be greatly appreciated,

Thanks,

Dru
Draw the graph of $\displaystyle D = 10 + 3 \sin \left(\frac{\pi t}{6}\right), 0 \leq t \leq 24$. Draw the graph of $\displaystyle D = 8.5$. The intervals for which $\displaystyle D \geq 8.5$ should be clear. And it should also be clear why you should now solve $\displaystyle 8.5 = 10 + 3 \sin \left(\frac{\pi t}{6}\right), 0 \leq t \leq 24$ ....