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 December 4th, 2011, 02:13 AM #1 Guest   Joined: Posts: n/a Thanks: I need help for my homework Trigonometric inequalities ? 1) sin x>sin3x , x ? (0,2pi) 2)sin x>\tan x , x ? (0,2pi) 3)$\frac{1-4sin^{2}x}{cos2x+cos x}\leq 2$ 4)$\tan^{2}x< \left | 1-2\cot^{2}x \right |$ , x ? (0,2pi) 5)$2cos x\leq \left | \sqrt{1+2sin2x}-\sqrt{1-2sin2x} \right |\leq \sqrt{2}$ 6)$\left | sin x \right |< \left | cos x \right |$ , x ? (0,2pi) 7) $sin x+\left | sin x \right |>1$ , x ? (0,2pi) Please do step by step help for these problems. I have tomorrow test urgent
 December 4th, 2011, 03:13 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond 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?.
 December 4th, 2011, 03:48 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond 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?
 December 4th, 2011, 12:15 PM #4 Senior Member   Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0 Re: I need help for my homework 3)$\frac{1-4sin^{2}x}{cos2x+cos x}\leq 2$ $1-4sin^{2}x\leq 2cos2x+2cos x$ $1-4(1-cos^{2}x)\leq 2(2cos^{2}x-1)+2cos x$ $1-4+4cos^{2}x\leq 4cos^{2}x-2+2cos x$ $-\frac{1}{2}\leq cos x$ ...
 December 4th, 2011, 12:26 PM #5 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 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? - unlocked -

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