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# Find an Equation for the Sine or Cosine Wave - Problem 1

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

I want to find the equation for another sine or cosine curve. I have one here and judging by the graph the fact that it starts on an x intercept I would say that this is a sine curve of some kind which means I’m going to have the equation y equals A times the sine of bx. It’s just a question of what A and b are.

Now because this curve goes downward instead or upward like sine normally does, I’m going to guess that there is a reflection across the x axis. In order to figure out what A is, I need to know that the amplitude of this is and it looks like it’s going to be 3/5. The coordinates to this point are the clue, the second coordinate the y coordinate of this point, 3/5. And if this distance is the same as this distance, then this will be negative 3/5 and that makes the amplitude 3/5.

So if I have a reflection across the x axis, and an amplitude of 3/5 that means A is negative 3/5, so y equals -3/5 sine of bx. I just need to find out what b is. The key to finding b is figuring out what the period of this function is. This point has an x coordinate of ¾ so well that’s ¾ all the way through a period, so this must be 1. If the period is 1 I use this formula, period equals 2 pi over b to find out what b is. I plug in 1 for the period and this one’s easy, I just multiply both sides by b and get b equals 2pi. That’s it, we’re done.

My final equation is y equals -3/5 sine of 2pi x. Let me move this guy over just a little bit, P. Y equals -3/5 sine of 2 pi x.

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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

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