trigonometric identities | Mathematics | Page 1

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tepid jasper May 6, 2024, 2:15 AM

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You don't even need to know any trigonometry for this one, just regular algebra.

inland fractal May 6, 2024, 2:15 AM

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oh...

tepid jasper May 6, 2024, 2:15 AM

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What do you have in the numerator?

inland fractal May 6, 2024, 2:16 AM

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i jst have no clue how to get started since its a bit longer than im used to and i got sin squared -1 in the numerator

tepid jasper May 6, 2024, 2:16 AM

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Okay, and what is that?

inland fractal May 6, 2024, 2:16 AM

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cos sqaured

tepid jasper May 6, 2024, 2:16 AM

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No it's not, but also that's not the answer I'm looking for.

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I'm looking for an algebraic answer.

inland fractal May 6, 2024, 2:17 AM

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u add 1 to both sides?

tepid jasper May 6, 2024, 2:17 AM

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...no.

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What does subtraction mean? What's the word for the result of a subtraction?

inland fractal May 6, 2024, 2:18 AM

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difference

tepid jasper May 6, 2024, 2:18 AM

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And what are you taking the difference of here?

inland fractal May 6, 2024, 2:19 AM

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um the sin squared? sorry im jst so stumped

tepid jasper May 6, 2024, 2:20 AM

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That's one thing.

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What's the other thing?

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You can't take the difference of one thing.

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Subtraction is a two-place operation.

inland fractal May 6, 2024, 2:21 AM

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tan??

tepid jasper May 6, 2024, 2:21 AM

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...so the numerator is sin^2(theta) - tan(theta)?

inland fractal May 6, 2024, 2:23 AM

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for the left side, its jst sin^2(theta)-1, if we need to do both sides then its sin^2(theta)-1 -sin(theta)+1

tepid jasper May 6, 2024, 2:23 AM

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We're only considering the left side because the entire point is to transform it into the right side.

inland fractal May 6, 2024, 2:25 AM

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so we dont need to transform sin^2-1 into cos^2 at all to have it as simplified as it can be? sorry if my answers are a little frustrating

tepid jasper May 6, 2024, 2:26 AM

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No, we don't, not least because it doesn't equal that anyway.

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So the numerator is sin^2(theta) - 1, you said?

inland fractal May 6, 2024, 2:26 AM

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oh i mixed them up, but yh so far

tepid jasper May 6, 2024, 2:27 AM

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What's the square root of 1?

inland fractal May 6, 2024, 2:27 AM

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1?

tepid jasper May 6, 2024, 2:27 AM

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Yes, the square root of 1, what is it?

inland fractal May 6, 2024, 2:27 AM

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oh, that was my answer...

tepid jasper May 6, 2024, 2:28 AM

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You're saying the square root of 1 is 1?

inland fractal May 6, 2024, 2:29 AM

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well to the top of my head yes and its also what google says :/

tepid jasper May 6, 2024, 2:29 AM

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Which means 1^2 = 1, right?

inland fractal May 6, 2024, 2:29 AM

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yes

tepid jasper May 6, 2024, 2:29 AM

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Therefore sin^2(theta) - 1 = sin^2(theta) - 1^2.

inland fractal May 6, 2024, 2:31 AM

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no offense and sorry if this sounds dumb but why was was it square rooted, was it to have it sqaured same as sin?

tepid jasper May 6, 2024, 2:31 AM

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...I was hoping you would recognize the structure.

inland fractal May 6, 2024, 2:31 AM

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...

tepid jasper May 6, 2024, 2:32 AM

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We have a difference. What do we have a difference of?

inland fractal May 6, 2024, 2:32 AM

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u able to put it in any other terms for me lmao

tepid jasper May 6, 2024, 2:32 AM

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Please answer my question.

inland fractal May 6, 2024, 2:33 AM

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i'll jst figure it out on my own, sorry for wasting ur time

indigo galeBOT May 6, 2024, 2:33 AM

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tepid jasper May 6, 2024, 2:33 AM

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Squares. We have a difference of squares.

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Do you not know what a difference of squares is?

inland fractal May 6, 2024, 2:34 AM

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no my teacher is a first year math teacher and never mentioned such a thing

tepid jasper May 6, 2024, 2:35 AM

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You're learning trigonometry in your first year of math? You mean to tell me you haven't learned any algebra?

inland fractal May 6, 2024, 2:36 AM

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no as in i have learned algebra, im in junior year learning pre cal but none my of teachers in the years before havent mentioned a difference in squares ever as long as i can remember

tepid jasper May 6, 2024, 2:36 AM

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So you've never seen a^2 - b^2 before?

inland fractal May 6, 2024, 2:38 AM

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tbh no, i might have but it might have been explained different

tepid jasper May 6, 2024, 2:38 AM

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...okay, well the rule is that a^2 - b^2 = (a - b)(a + b).

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You can see that yourself by multiplying out the right side.

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Therefore, sin^2(theta) - 1 equals what?

inland fractal May 6, 2024, 2:40 AM

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it equals (sin - 1) (sin + 1)

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?

tepid jasper May 6, 2024, 2:40 AM

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Exactly.

inland fractal May 6, 2024, 2:40 AM

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ah okkk

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we are getting somewhere, sorry for all this

tepid jasper May 6, 2024, 2:41 AM

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It's not your fault if you weren't taught this.

inland fractal May 6, 2024, 2:41 AM

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onto the denominator?

tepid jasper May 6, 2024, 2:41 AM

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So now what do you notice about the denominator?

inland fractal May 6, 2024, 2:42 AM

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uhh tan is multiplaying by sin and then sin minus tan?

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tan x sin - tan basically*

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the subtraction part?

tepid jasper May 6, 2024, 2:43 AM

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So what can we do with that?

inland fractal May 6, 2024, 2:44 AM

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separate them?!

tepid jasper May 6, 2024, 2:44 AM

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I'm not sure what you mean by that.

inland fractal May 6, 2024, 2:45 AM

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oh forget it then(as in turn it into two fractions) we can algebrically get rid of them by adding tan?

tepid jasper May 6, 2024, 2:45 AM

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How do we add things to a denominator?

inland fractal May 6, 2024, 2:47 AM

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can i just say I dont know so i dont keep guessing from this point forth and make this longer or u want me to keep guessing cuz to be honest. I don't Know.

tepid jasper May 6, 2024, 2:47 AM

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Yes, please say you don't know if you don't know.

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Don't guess.

inland fractal May 6, 2024, 2:47 AM

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alright thank you

tepid jasper May 6, 2024, 2:47 AM

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So we have a difference of things, both of which have a factor of tan(theta).

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tan(theta) * sin(theta) - tan(theta) * 1.

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So... it's just the distributive property.

inland fractal May 6, 2024, 2:50 AM

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tan^2 - tan) (sin x tan (sin?

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how would i distribute sin to tan?

tepid jasper May 6, 2024, 2:50 AM

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...what? Why are you squaring anything?

inland fractal May 6, 2024, 2:51 AM

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I dont know, it seems i have learned distributive property wrong

tepid jasper May 6, 2024, 2:51 AM

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a(b + c) = ab + ac

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That's the distributive property.

inland fractal May 6, 2024, 2:52 AM

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where do we go from here

tepid jasper May 6, 2024, 2:53 AM

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tan(theta)sin(theta) - tan(theta)*1 = ?

inland fractal May 6, 2024, 2:54 AM

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ah alright, we keep the left side the same but jst add the 1 to multiply to tan

tepid jasper May 6, 2024, 2:54 AM

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...no, what does that equal, per the distirbutive property?

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You are writing all this down, right?

inland fractal May 6, 2024, 2:55 AM

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yh im done with this, have a good night and sorry for wasting ur time

tepid jasper May 6, 2024, 2:55 AM

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Dude, we're so close.

#trigonometric identities