Question 1091305
<br>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<br>
{{{y = (5/2)sin((1/2)(x-45))-2}}}<br>
The standard form for this kind of function is<br>
{{{y = (a)sin((b)(x-c))+d}}}<br>
Where
a is the vertical stretch;
b determines the horizontal stretch;
c is the horizontal shift; and
d is the vertical shift<br>
The order in which the transformations are applied is the order in which you would evaluate the expression for a given input value.<br>
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.