![]() ![]() You cannot solve for phase shift given ONLY the maximum and minimum values, so I think you may also be given the points where those maximum and minimum values occur. Phase shift c is best discovered by pattern matching if you are given an equation, or by examining values when sin equals a significant point such as zero or maximum or a minimum. Once you become familiar with how it works it will be easier to work with the calculations. ![]() If all else fails, graph a few points with pencil and paper. A graphing calculator works well for this, especially if you use one of the ones on line that will give you different colors. Pick an obvious marker point, such as where the maximum is on the unshifted function and where the function equals zero. Horizontal shift can be counter-intuitive (seems to go the wrong direction to some people), so before an exam (next time) it is best to plug in a few values and compare the shifted value with the parent function. Horizontal shift for any function is the amount in the x direction that a function shifts when c ≠ 0. When you graph "sin(x-10)" you are plotting "sin(x-10 radians)" at the x coordinate "x radians", so you're getting y values using an x that is 10 radians to the left of where you are on the x axis (y=sin(-7 radians) for x = 3 radians, y = sin(-1 radian) for x = 9 radians, y = sin(-15 radians) for x = -5 radians, etc.), which shifts the graph to the right 10 radians. Thus, you are getting y values from 10 radians to the right of where you are on the x axis (y=sin(13 radians) for x = 3 radians, y=sin(19 radians) for x=9 radians, y=sin(5 radians) for x= -5 radians, etc.), which shifts the graph to the left by 10 radians. When you graph, say, "y = sin(x+10)", you are plotting the value of "sin(x+10 radians)" at the x coordinate "x radians". In these graphs of sine functions, x stands for theta on the unit circle and is the independent variable. Theta is defined as the angle with sine y/r (= y), or with cosine x/r (= x). On the unit circle if we know x than we can get +-y and if we know y we can get +-x. ![]()
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