SOLUTION: For the function y=5/2sin(1/2x-22.5 degrees)-2 , State the transformations, in the order you would apply them. [2] • ___________ ___________ ___________ ___________

Algebra ->  Trigonometry-basics -> SOLUTION: For the function y=5/2sin(1/2x-22.5 degrees)-2 , State the transformations, in the order you would apply them. [2] • ___________ ___________ ___________ ___________      Log On


   

Question 1091305: For the function y=5/2sin(1/2x-22.5 degrees)-2 , State the transformations, in the order you would apply them. [2]
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Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!

First, you need to modify the argument for sine so that it is in the form p(x-q); then the q is the horizontal shift and the p determines the horizontal stretch or compression. So write the function as

y+=+%285%2F2%29sin%28%281%2F2%29%28x-45%29%29-2

The standard form for this kind of function is

y+=+%28a%29sin%28%28b%29%28x-c%29%29%2Bd

Where
a is the vertical stretch;
b determines the horizontal stretch;
c is the horizontal shift; and
d is the vertical shift

The order in which the transformations are applied is the order in which you would evaluate the expression for a given input value.

The innermost parentheses is (x-45); so apply the horizontal shift first.
Next is the multiplication (of the angle) by 1/2; so apply the horizontal stretch second.
Next is the multiplication (of the sine) by 5/2; so apply the vertical stretch third.
And last is subtracting 2, which is the same as adding -2, so apply the vertical shift last.