what is the value when t=0?
cos has a normal period of 2pi so when does pi/14 * t = 2pi?
I know that a full revolution around the unit circle is equal to 2pi
then cos(2pi) is one complete revolution therefore, we simply need to determine when pi/14*t = 2pi
How would I find that, though?
simple algebra ....
multiply both sides by .... what?
well, 14/pi would wipe out the pi/14 so ... lets say t = 2pi * 14/pi makes one full revolution
Okay, I understand. What do I do from there?
simplify .. what is 2pi * 14/pi?
Would pi cancel out?
yes, even tho thats a bad word to apply ... pi/pi = 1, so there is nothing to actually 'cancel'. but yeah
Alright, so when pi/pi = 1, that leaves 2 *14 = 28
correct, so it takes a time period of 28 to make one full revolution right?
so part 2 is done, what was part 1?
Using the equation, I substituted 0 in for the value of t, since the ride has not started yet. The new equation will then look like, H(0) = 25 cos(pi/14 * t) + 31. Simplifying, the height of Sandra when t = 0 is 56 feet
25+31 = 56 .. i agree now what do you know about the min and max of a cos(u) ?
I don't know anything about that
really? you have unit circle right?
or at least are able to graph y = cos(x)
Yes, but I'm not technically in trig. I'm actually in Algebra 2. This is just an intro to trig, I guess
I'm not great at graphing either
well, the unit circle, tells us cosine from left to right ... |dw:1442188466506:dw| unit is another way of saying 1, the unit circle has a radius of 1
cos alternates from 1 to -1 to 1 to -1 ... etc so its max is 1, its min is -1 how can we use this in part3?
I'm so sorry, but I have absolutely no clue
hmm, cos(pi/14*t) has a minimum value of -1. so use it 25(min of cos) + 31 gives us?
25(-1) + 31 is 6 yes
Thanks for your help!