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I think the objective is to determine the interval or intervla on which sin x > cos x. Graph both sin x and cos x on the same set of axes. Mark them (sin x, cos x). It should be obvious where sin x > cos x. Identify the interval(s) on which this inequality is true.
i still dont get it..
Look at the graphs of sin x and cos x in the link above.
Let's look at the first inequality, \(\sin(x)>\cos(x)\). If we plot the lines \(\sin(x)\) and \(\cos(x)\) on a graph we get this graph. The red line is \(y=\sin(x)\) and the blue is \(y=\cos(x)\). We want to find the values of \(\sin(x)>\cos(x)\), so where is the red line above the blue line?
the sin x is in the same spot?
I don't understand what you're asking. Can you see where the red line is above the blue line?
i think so. the link you sent is sin x = cos x?
im really confused on how to draw sin x > cos x and <
No, the link I sent is plotting y=sin(x) in red and y=cos(x) in blue. Can you see that the red line is above the blue line between points A and B in this graph: https://i.imgur.com/FFcxDv8.png
ok yes i see that
Do you know how to graph inequalities?
i dont remember
do i need to shade something for the inequalities?
Read this: http://www.purplemath.com/modules/ineqgrph.htm The region between \(A\) and \(B\), where \(sin(x)>cos(x)\) is what we need to shade. I can't work out how to plot this nicely for you so I'll draw it:|dw:1449459172357:dw|
But note, because it's greater than not greater than or equal to, the bottom line of the shaded region should be dashed - I just couldn't easily draw it here.
thanks for your help
No problem. Do you understand how to do sin(x)
I think so
Great, glad to hear it. Just as a supplementary bit of information, what @mathmale was speaking about, if we want to find the values of \(x\) such that \(\sin(x)>\cos(x)\) then we need to find what the interval (A,B) is (non inclusive because it's just greater than, not equal to). To find these points, we solve \(\sin(x)=\cos(x)\) which is just \(\tan(x)=1\) so \(x=45, 225, 405...\) So we know the distance between these points is 180 degrees. We also know it repeats itself every 360 degrees (because that's the period of cos and sin), so we know our intervals satisfying this inequality are \((45+360n, 225+360n)\) for \(n \in Z\).
The graph of sin x > cos x only takes into account the x values for which sin x > cos x, so the graph is simply points on the x-axis (number line). The solution of the inequality is an infinite number of intervals on the x-axis. |dw:1449500308915:dw|