# Math Help - Trig Word Problem

1. ## Trig Word Problem

Hey, just stopping by, need some help on a review question and any help would be appreciated.

Question:

The following describes the height in, in meters, of a cart on a ferris wheel as a function of time, in seconds.

H = 10sin[30(t-3)]+11.5

Determine the time it takes a person to reach a height of 16m.

I know to plug 16 in for H, but what do I do from there to solve for t?

2. Originally Posted by RyanOwnage
Hey, just stopping by, need some help on a review question and any help would be appreciated.

Question:

The following describes the height in, in meters, of a cart on a ferris wheel as a function of time, in seconds.

H = 10sin[30(t-3)]+11.5

Determine the time it takes a person to reach a height of 16m.

I know to plug 16 in for H, but what do I do from there to solve for t?
well, you begin by solving for the sine. then take the arcsine to solve for what was being sined. you'd end up with:

30(t - 3) = arcsin(...)

you can find the arcsine from your calculator and then it would be easy to solve for t from there

can you continue?

3. Bit confused

Could you possibly show me the first couple of steps?

Thanks again.

4. Originally Posted by RyanOwnage
Bit confused

Could you possibly show me the first couple of steps?

Thanks again.
$16 = 10 \sin [30(t - 3)] + 11.5$ ......subtract 11.5 from both sides

$\Rightarrow 4.5 = 10 \sin [30(t - 3)]$ ...........divide both sides by 10

$\Rightarrow 0.45 = \sin [30(t - 3)]$ ..........take the arcsine of both sides

$\Rightarrow 30(t - 3) = \arcsin (0.45)$
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5. Thank you very much, got it solved