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December 4th, 2011, 02:13 AM   #1
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I need help for my homework

Trigonometric inequalities ?

1) sin x>sin3x , x ? (0,2pi)

2)sin x>\tan x , x ? (0,2pi)

3)

4) , x ? (0,2pi)

5)

6) , x ? (0,2pi)

7) , x ? (0,2pi)

Please do step by step help for these problems. I have tomorrow test
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December 4th, 2011, 03:13 AM   #2
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Re: I need help for my homework

1) sin(x) > sin(3x)

sin(3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos²(x) + cos²(x)sin(x) - sin³(x) = cos²(x)(2sin(x) + sin(x)) - sin³(x) = 3sin(x) - 4sin³(x).

sin(x) > sin(3x)

4sin³(x) - 2sin(x) > 0

2sin(x)(2sin²(x) - 1) > 0 ? ?/4 < x < 3?/4, ? < x < 5?/4, 7?/4 < x < 2?.
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December 4th, 2011, 03:48 AM   #3
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Re: I need help for my homework

2) sin(x) > sin(x)/cos(x). If sin(x) is positive and cos(x) is negative (second quadrant), the inequality holds. If sin(x) is negative and cos(x) is positive (fourth quadrant), the inequality holds, because 0 < cos(x) < 1. tan(x) isn't defined for x such that cos(x) = 0.

Will you make an attempt at some of the remaining problems, and post your working?
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December 4th, 2011, 12:15 PM   #4
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Re: I need help for my homework

3)




...
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December 4th, 2011, 12:26 PM   #5
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Re: I need help for my homework

Wait... WHO is taking the test tomorrow?
Because unless you are able to video chat with one of us during the test, you might need to learn this for yourself!

For why I am closing this, see the posts:
viewtopic.php?f=37&t=19563
viewtopic.php?f=37&t=19955

Edit:
The motivation for closing this thread was to discourage the posting of many questions on one thread, without demonstrating any work, and expecting the other users to spoon-feed answers. Of course, I don't want to impede the learning process!

Let's try to determine, for each problem,
a) What TYPE of problem is this? Is there a commonly used description that we can web search for more insight into the problem solving process?
b) Where are you STUCK?
c) What other (similar) EXAMPLES have you seen?



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