Each function graphed is of the form y = c + cos x, y = c + si...

Question

Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.

Accepted Answer

Welcome back everyone. In this problem. If the trigonometric function shown as the possible forms of Y equals D plus sine, XY equals D plus the cosine of XY equals the sine of X minus C or Y equals the cosine of X minus C. What is the equation that represents the graph note that C should have the smallest possible positive value for our answer choices A says that it's Y equals five plus the cosine of XB says it's Y equals negative five plus the sine of XC says it's Y equals the sine of X minus 1/5 of pi. And D says it's Y equals the cosine of X minus 1/5 of pi. Now, before we try to figure out which one of those it is, let's try to understand our graph here. So first of all, by looking at our graph notice that this waveform this trigonometric function, it closely resembles the graph of Y equals the sine of X where we know that Y equals the sine of X would look something like this. OK. It would look something like that. So it looks like the sign function. But what's the difference here? We notice that instead of starting at zero units on the X and the Y axis, it starts at negative one, negative, two, negative three, negative four, negative five units on the Y axis. OK. So it's like the sine graph but it has been translated downward. Let's, let's make sure we show that here. It's been translated downward by five units. Now, what do we know about vertical translations? We call that for a trigonometric function. For a trigonometric function Y equals F of X. OK. Then Y equals D plus F FX. OK. Represent, let me put that back in back here represents a vertical translation by D units where if D is positive it moves upwards and if D is negative, it moves downwards here. By comparison, we can tell that D or constant or shift equals negative five. So since D equals negative five, if we substitute that into our general form, what we're saying is that the equation of our graph is going to be equal to negative five plus the sine of X. If we look back on our answer choices that would have been answer choice B therefore the equation Y equals negative five plus sine X represents our graph. Thanks a lot for watching everyone. I hope this video helped.

Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.

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Key Concepts

Trigonometric Functions

Vertical and Horizontal Shifts

Phase Shift

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