Quandaries and Queries


Name: Eman

Who is asking: Student
Level: Secondary

Hi there,

I am stuck on this question having many parts, the problem is I know how to do all the parts once i get through the fist line!!!

here it is..(the first part)

Q : Sketch the graph of y = 1 - sin(x+60). for 0 <= x<= 360, giving the coordinates of the maximum and minimum points and the pints where the curves crosses the y axis.

<= means 'less than equal to'

This is an AS level question.

Please help me soon, because I am studying through correspondense and there are not many to help me here. Thank you so much!!!



Hi Eman,

I am going to build the graph from the graph of the sine function. I see the sine function as the graph

y = sin(angle)

where the graph crosses the horizontal axis when the angle is 0, 180, 360, ... (I put a red dot on the horizontal axis at 60 degrees.)

For a graph of sin(x + 60) with 0 <= x<= 360, the angle starts at 60 degrees and ends at 360 + 60 = 420 degrees. Thus the graph of y = sin(x + 60) for 0 <= x<= 360 is

y = sin(x + 60)

But you need y = - sin(x + 60), so all the positive values of y become negative and the negative values become positive. Hence the graph is

y = - sin(x + 60)

One last step. What you want is y = 1 - sin(x + 60), so you need to add 1 to each y-value on the graph. Hence the final graph is

y = 1 - sin(x + 60)


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