Circular functions help

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kamil9876

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Re: Circular functions help

« Reply #15 on: August 21, 2009, 10:09:28 pm »

0

Because TT despises graphs and adores algebraic alternatives:
$<br />-1\leq sin2x \leq 1$ (can take on any values in this range)

$0 \leq |sin2x| \leq 1$
$-3 \leq -3|sin2x| \leq 0$

adding 3 to both sides:

$0 \leq -3|sin2x| + 3 \leq 3$

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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

TrueTears

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Re: Circular functions help

« Reply #16 on: August 21, 2009, 10:10:02 pm »

0

Quote from: kamil9876 on August 21, 2009, 10:09:28 pm

Because TT despises graphs and adores algebraic alternatives:
$<br />-1\leq sin2x \leq 1$ (can take on any values in this range)

$0 \leq |sin2x| \leq 1$
$-3 \leq -3|sin2x| \leq 0$

adding 3 to both sides:

$0 \leq -3|sin2x| + 3 \leq 3$

LOL I just showed him that on msn

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PhD @ MIT (Economics).

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