anonymous
  • anonymous
how to graph sin x > cos x? and sin x < cosx?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmale
  • mathmale
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.
anonymous
  • anonymous
i still dont get it..
mathstudent55
  • mathstudent55
http://www.wolframalpha.com/input/?i=y+%3D+cos+x%3B+y+%3D+sin+x

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

mathstudent55
  • mathstudent55
Look at the graphs of sin x and cos x in the link above.
anonymous
  • anonymous
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?
anonymous
  • anonymous
the sin x is in the same spot?
anonymous
  • anonymous
I don't understand what you're asking. Can you see where the red line is above the blue line?
anonymous
  • anonymous
i think so. the link you sent is sin x = cos x?
anonymous
  • anonymous
im really confused on how to draw sin x > cos x and <
anonymous
  • anonymous
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
anonymous
  • anonymous
ok yes i see that
anonymous
  • anonymous
Do you know how to graph inequalities?
anonymous
  • anonymous
i dont remember
anonymous
  • anonymous
do i need to shade something for the inequalities?
anonymous
  • anonymous
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|
anonymous
  • anonymous
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.
anonymous
  • anonymous
thanks for your help
anonymous
  • anonymous
No problem. Do you understand how to do sin(x)
anonymous
  • anonymous
I think so
anonymous
  • anonymous
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 \(n \in Z\).
anonymous
  • anonymous
i graphed sin x = cos x
mathstudent55
  • mathstudent55
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|

Looking for something else?

Not the answer you are looking for? Search for more explanations.