heights of objects

**belloway** · January 1st 2010, 09:05 PM

The heights h (in feet) of two people in different seats on a ferris wheel can be modeled by h1=28cos10t+38 and h2=28cos(10(t-Pie/6))+38, 0 is less than or equal to t and 2 is greater than or equal to t. t is the time ( in minutes). When are the two people at the same height?

this is another one that has been stumping me
thanks again for the help

**Amer** · January 2nd 2010, 12:42 AM

Originally Posted by belloway

The heights h (in feet) of two people in different seats on a ferris wheel can be modeled by h1=28cos10t+38 and h2=28cos(10(t-Pie/6))+38, 0 is less than or equal to t and 2 is greater than or equal to t. t is the time ( in minutes). When are the two people at the same height?

this is another one that has been stumping me
thanks again for the help

$h_1= 28\cos 10t + 38$

$h_2= 28\cos 10\left(t-\frac{\pi}{6}\right) + 38$

same height

$h_1 = h_2$

$28\cos 10 t +38 = 28\cos 10\left(t-\frac{\pi}{6}\right) + 38$

$\cos 10t = \cos 10\left(t-\frac{\pi}{6}\right)$

use the identity

$\cos a-b = \cos a \cdot \cos b + \sin a \cdot \sin b$

after you use it and simplify you will get

$\cos 10 t = -\sqrt{3} \sin 10t$

$\tan 10 t = \frac{-1}{\sqrt{3}}$

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