FIRST OF ALL, you must remember that trigonometric functions like sine, cosine and tangent are periodic. In other words, they are continuous with the same pattern =D think of eternal~
I would say this part of math is fairly easy to understand. But it's just the matter of understanding and knowing it well without memorizing.
Remember how polynomial functions could have their transformations? Like the vertical stretch, horizontal shift, etc? Trigonometric functions can too. But there are 'special ways' to understand their transformation. Not that much of a difference, its just the way to find the value of each transformation.
Before that, note there are 3 graphs at the top. Now, these 3 graphs are all trigonometric graphs over ONE CYCLE.
What is a PERIOD?
A period is basically the x value at the end of a cycle (from the beginning of the first cycle to the end of the first cycle). In this case, the period for sinx graph is 2pi, for cosx graph is 2pi, and pi for the tanx graph. It means how 'long' it takes for one cycle to be completed.
What is an AMPLITUDE?
An amplitude is like the 'height' of the graph from the x axis. Ask yourself "How high and how low does the graph go, in terms of the y values?" and you will get the amplitude of the graphs. In this case, the amplitude for the sinx graph is 1unit, for the cosx graph is 1unit, and 1 unit as well for the tanx graph.
To refresh,
y = a sin k (x - d) + c, where
a = vertical stretch / vertical compression
k = horizontal stretch / horizontal compression
d = horizontal shift (left if +, and right if -)
c = vertical shift (upwards or downwards)
Normally, the questions asked in this topic will ask for a new equation based on the information they provide you with, such as the vertical shift, horizontal compression and more. All you need to do is just to fill in the value they provide at the correct space in the general equation. For example,
A sine function has a vertical stretch of 2.
Hence, the equation of the function is y = 2sinx
However, sometimes they give you the period of the graph and expect you to find its horizontal stretch/compression. Then comes the formula
Period = 2pi / k, where k is the horizontal stretch/compression.
For example,
Find the value of k if the period is 2pi
Hence, 2pi = 2pi / k >>> k = 4.
y = sin4x
Simple as that! If you need more help, Click Here for a YouTube Tutorial
Bye!
I would say this part of math is fairly easy to understand. But it's just the matter of understanding and knowing it well without memorizing.
Remember how polynomial functions could have their transformations? Like the vertical stretch, horizontal shift, etc? Trigonometric functions can too. But there are 'special ways' to understand their transformation. Not that much of a difference, its just the way to find the value of each transformation.
Before that, note there are 3 graphs at the top. Now, these 3 graphs are all trigonometric graphs over ONE CYCLE.
What is a PERIOD?
A period is basically the x value at the end of a cycle (from the beginning of the first cycle to the end of the first cycle). In this case, the period for sinx graph is 2pi, for cosx graph is 2pi, and pi for the tanx graph. It means how 'long' it takes for one cycle to be completed.
What is an AMPLITUDE?
An amplitude is like the 'height' of the graph from the x axis. Ask yourself "How high and how low does the graph go, in terms of the y values?" and you will get the amplitude of the graphs. In this case, the amplitude for the sinx graph is 1unit, for the cosx graph is 1unit, and 1 unit as well for the tanx graph.
To refresh,
y = a sin k (x - d) + c, where
a = vertical stretch / vertical compression
k = horizontal stretch / horizontal compression
d = horizontal shift (left if +, and right if -)
c = vertical shift (upwards or downwards)
Normally, the questions asked in this topic will ask for a new equation based on the information they provide you with, such as the vertical shift, horizontal compression and more. All you need to do is just to fill in the value they provide at the correct space in the general equation. For example,
A sine function has a vertical stretch of 2.
Hence, the equation of the function is y = 2sinx
However, sometimes they give you the period of the graph and expect you to find its horizontal stretch/compression. Then comes the formula
Period = 2pi / k, where k is the horizontal stretch/compression.
For example,
Find the value of k if the period is 2pi
Hence, 2pi = 2pi / k >>> k = 4.
y = sin4x
Simple as that! If you need more help, Click Here for a YouTube Tutorial
Bye!
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