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Amplitude, phase and vertical shift.

Dear experts,

I am studying trigonometry functions.

In trigonometry functions, we have y=sin-theta and y=a.sin (3.theta + 30 degrees) + 60 degrees

I understand that when y=sinx we use the unit circle with radius of 1unit to explain radian/amplitude.

I am trying to under the following concepts of amplitude, phase shift and vertical shift. I understand the concept of period for trigonometric functions.

Now is there a sequence of videos or notes which will help me understand these concepts. Not just the calculations but also the implications of unit circle and on the trigonometry functions. My struggle is not just to crunch numbers but also to understand the concepts how the numbers are impacting the trigonometric functions.

Kindly guide.

CompProbSolv

"I understand that when y=sinx": make sure you understand where cos and tan come from with the unit circle. That will help with some the relationships between them.

I wouldn't really put amplitude and vertical shift in the realm of trig, though phase shift could apply. You can model phase shift on the unit circle (add or subtract the appropriate angle), but I'm not sure that helps.

You really need to be looking at a graph with amplitude vs. angle (or time) as the line in the unit circle rotates. A sine or cosine wave will have the smooth, symmetrical up and down shape as you move along the X axis. The amplitude is the vertical height of the wave (commonly measured from peak-to-peak). Phase shift would be the wave sliding to the right or left along the X axis. Vertical shift would be the wave sliding up or down along the Y axis. "Standard" sine or cosine waves are symmetrical around the X axis. Once you have vertical shift, it's no longer symmetrical.

This will give you some information that may make it understandable: https://en.wikipedia.org/wiki/Sine_wave .

aburr

The following link will give you access to MANY good notes on almost every math concept ( and many other subjects)

Library - Khan Academy | khanacademy.org
https://www.khanacademy.org/library

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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