precalculus help | Mathematics | Page 1

old grailBOT Jul 15, 2024, 5:33 AM

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digital sinew Jul 15, 2024, 5:35 AM

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for 1

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tan(t)=2

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what is the period of tan?

marsh harness Jul 15, 2024, 5:41 AM

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digital sinew what is the period of tan?

Sorry I edited it, it’s tan (t) = 1 and your finding tan (t + pie )

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So one period

timber estuary Jul 15, 2024, 5:51 AM

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$$ \tan (x+\pi) = \frac{\tan x + \tan \pi}{1-\tan x\tan \pi} = \tan x $$

snow sageBOT Jul 15, 2024, 5:52 AM

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aL

timber estuary Jul 15, 2024, 5:52 AM

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@marsh harness

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$$ \tan (-t + 2\pi) = \tan (-t) = \frac{\sin (-t)}{\cos (-t)} = -\frac{\sin t}{\cos t} = -\frac{\sqrt{1-\cos ^2t}}{\cos t} $$

snow sageBOT Jul 15, 2024, 5:53 AM

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aL

marsh harness Jul 15, 2024, 5:53 AM

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It’s by using the periodic properties and even/odd identities

timber estuary Jul 15, 2024, 5:54 AM

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snow sage **aL**

what do you conclude about period of tan from these equalities?

marsh harness Jul 15, 2024, 5:55 AM

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That’s why I came here, lol

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From seeing the questions I believe tan being 1, it equals to pie/4 + a period

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But I’m uncertain if there is more to do or not

timber estuary Jul 15, 2024, 5:56 AM

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if tan (t) = 1, then tan (t+pi) =x

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what is x?

marsh harness Jul 15, 2024, 5:57 AM

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It’s not given, I believe we have to find t which may be pie/4

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Pi/4 + pi

timber estuary Jul 15, 2024, 5:58 AM

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you dont have to know what t is

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it is enough to know that tan (t) = 1 and tan is pi-periodic

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conclusion?

marsh harness Jul 15, 2024, 5:58 AM

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But is the answer simply 1 then?

timber estuary Jul 15, 2024, 5:58 AM

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yes!

timber estuary Jul 15, 2024, 5:59 AM

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snow sage **aL**

see this, as well

marsh harness Jul 15, 2024, 5:59 AM

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Alright I think I understand a bit

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If the first answer is 1 what would be the others?

timber estuary Jul 15, 2024, 6:00 AM

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this is what you wrote

marsh harness Jul 15, 2024, 6:00 AM

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Yep

timber estuary Jul 15, 2024, 6:01 AM

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the question in the picture is different

marsh harness Jul 15, 2024, 6:01 AM

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Oh I apologize

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Let me re-edit it

timber estuary Jul 15, 2024, 6:01 AM

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$$ \cos (a+b) = \cos a\cos b - \sin a\sin b $$

snow sageBOT Jul 15, 2024, 6:01 AM

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aL

marsh harness Jul 15, 2024, 6:02 AM

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What is that equation?

timber estuary Jul 15, 2024, 6:02 AM

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relevant to 2.

marsh harness Jul 15, 2024, 6:03 AM

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But the question is simply asking of periodic properties and even/odd identities

timber estuary Jul 15, 2024, 6:03 AM

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what do you think the period of cosine is?

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and if you're not certain, how do you prove it?

marsh harness Jul 15, 2024, 6:04 AM

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Seeing cos is an even property it would be 0.25

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And seeing as sin is a negative property it would be 0.9 or -0.9

timber estuary Jul 15, 2024, 6:05 AM

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negative?

marsh harness Jul 15, 2024, 6:06 AM

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I’m uncertain, I have to revisit it again

timber estuary Jul 15, 2024, 6:06 AM

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cos is 2pi-periodic and even, therefore cos (-t) = cos (-t +2pi) = 0.25
sin is 2pi-periodic and odd, therefore sin (-t+2pi) = sin (-t) = -sin t = -0.9

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you don't say "cos is an even property"

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that is meaningless wordsoup

marsh harness Jul 15, 2024, 6:07 AM

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Sorry, my apologies

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May I ask you to help me with other questions?

timber estuary Jul 15, 2024, 6:08 AM

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sure, if this one is solved, close it and open a new question 🍺

marsh harness Jul 15, 2024, 6:09 AM

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Alright

#precalculus help