Double Angle Identities & Formulas of Sin, Cos & Tan - Trigonometry

[@TheOrganicChemistryTutor]

Trigonometry - Free Formula Sheet: bit.ly/47diggI Trigonometry - Basic Introduction: kzbin.info/www/bejne/nWm5dHuliNBoldE How To Graph Trig Functions: kzbin.info/www/bejne/nIKzgHWFe8dlqbs Evaluating Inverse Trig Functions: kzbin.info/www/bejne/qaCchZ2ha6yUaLc Verifying Trigonometric Functions: kzbin.info/www/bejne/hHaZq5aAiL-bjpI Trigonometry Final Exam Review: kzbin.info/www/bejne/hXLWk6tqiaqhgpI Next Video: kzbin.info/www/bejne/jZmamYCVe9iBabs

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[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a fantastic video on Double Angles Identities and Formulas of Sine, Cosine and Tangent.

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[@alster724]

For cos 2x there are 3 possible formulae 1.) cos 2x = cos²x-sin²x The next two are obtained from Pythagorean Identities First cos²x = 1-sin²x cos 2x= 1-sin²x-sin²x 2.) cos 2x = 1-2sin²x And also sin²x= 1-cos²x Reverting to the first formula and substitution we get cos 2x = cos²x-(1-cos²x) We finally have 3.) cos 2x = 2cos²x-1

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[@lexluther1219]

I was so afraid I would not understand how to do this. I kept telling myself nothing is impossible! I watch your videos and feel like I can learn even the most confusing topics. My teachers are no help of showing how they got an answer- they only show the answers. Thank you for making this so simple to understand!

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[@CKDesigner2525]

I like the cool way you used to prove the double angle identities, thank you!

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[@shaynerushton214]

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The sin 2x/cos 2x is the best trick for tan 2x

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Complete Formula; for sine - 0:51 for cosine - 1:51 for tagent -2:51

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@TheOrganicChemistryTutor @8:10 why did you multiply the numerator and denominator by 16 instead of creating common denominators and multiply by the reciprocal? I fully understand that your method is valid and a slightly different approach, I've just never taught it this way.

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My only problem is finding this out right at night before the test 😩

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Best tutor well explained

[@ilanmusk3503]

how do you know what type of triangle you have?

[@ilhamo_3427]

theres only 2 triangles, the first one has two 45 degrees and one that is 90 degrees. and the other one has 60 and 30 degrees and one 90 degrees. so in conclusion there's onyl 3 angles that you can only use when finding the exact value of any of the trigonometric ratios. you cannot write any other angle. OR.. you can just skip the special triangles and type the trigonometric ratio with its angle on the calculator and you'll get the exact value with that. one thing to keep in mind is if the answer was √a/a on the calculator you write 1/√a instead. FOR EXAMPLE; tan(30) = √3/3 *on calculator* but if you use the special triangle you will get 1/√3. hope that made sense.

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[@boostaddict_]

So these videos are great and all but one of the questions I'm having to answer, is simplifying 6 sin 5x cos 5x. Would the sin 5x be 5 sin theta cos theta, instead of 2? I have 0 ideas for how to do the cos 5x lol. Maybe 5 cos^2 theta - 1?

[@boostaddict_]

nope, just realized it was a multiple of sin 2x lmao. It's 3 sin 10x.

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Thanks for helping.

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Dead

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[@joshuabacchus4426]

How do u know which quadrant the angles fall in... I don't know how to tell.

[@d8264]

Compare angles to unit circle.

[@Meggutz]

Joshua Bacchus Pi is equal to 180 Quadrant 1 - 0 to 90 Quadrant 2 - 90 to 180 Quadrant 3 - 180 to 270 Quadrant 4 - 270 to 360

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@@Meggutz this was very useful thx

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Organic Chemistry Teacher is literally superior to my teacher.

[@jaychoro8159]

Why isn't Cosine positive since its in quadrant 4?

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May God bless you!

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Big help sir🙏🏻

[@latifaalrajhi3255]

3:54 how did you get the 4?

[@Gerry363c]

Example number 2 when finding cos2Q.. I think you had to distribute the negative which would’ve resulted to 169/169.. I may be wrong

[@beatricechipata765]

The 144/13 has a negative of course but it’ll be squared which will make it positive.

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[@naomiparsons462]

Why would you want sin(2x), or cos(2x) or tan(2x)? How can you use this information? I'm learning trig purely off KZbin so I don't know these things.

[@Buddhabebop]

why isnt the hypotenuse of the 5-12-13 triangle at 10 minutes negative? its in the 4th quadrant after all

[@qquamau7]

someone please tell me why only the 12 was negative in the fourth quad while 5 and 12 were exempted

[@shamsaali9629]

Yea i need to know too

[@gabyzamora5297]

THANK YOU

[@AmberRathour366]

At 9:43 Why isn't the hypotenuse negative?

[@supremechair5812]

The hypotenuse is positive no matter which quadrant it is in.

[@liwiikiwii]

how can you determine the type of triangle that it is?

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[@123pEpicGuy]

Helped so much.Thnx

[@ChasinNorthernLights]

So my teacher said we have to find the quadrants before solving the problem. But I don't know why?

[@meriiea]

because finding the quadrant first lets u know what sign ur answer needs to be. so if the quadrant is 3 and you're finding the value of cosine, then you don't have to worry about signs while figuring out the value and just put the negative sign at the final answer, (since cosine is always negative in quadrant 3). the trick is: ASTC. A= all positive in Q1. S= sine and csc positive in Q2, everything else negative. T= tangent and cot positive in Q3, everything else negative. C= cosine and sec positive in Q4, everything else negative. hope this helps :)

[@QuangNguyen-dw9je]

0:07 No I don't remember that equation

[@patriceestacio3650]

Thank you thank you thank you

[@mocha---]

cos(2x) = 2cosx-2sinx

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thank youuuuu

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❤️❤️❤️THANK YOU

[@phil331]

the question is sin x = 1/7 so I did the formula and got sin 2x = 10 sqrt2 / 49 but my homework says its wrong i cant figure out why

[@tabiosmariojr.6412]

what if the question is secant, cosecant and cotangent

[@tobiasmekpee8568]

What if there is a question that requires the answer like if there is given (sin tita=3/5) and (cos tita - 4/5).The cos2tita =7/25...my question is how can we make reciprical to find its (sin tita=3/5)and (cos tita - 4/5)..please help me..

[@ilhamo_3427]

whats the question exactly?

[@salvinsyed2831]

I don't understand how you figure out what quadrant theta is in

[@mocha---]

sin(x+y) = sinxcosy + sinycosx

[@Rose-hq5zk]

how tan could be positive while theta is in q4? 12:56

[@mocha---]

sin(2x) = 2sinxcosx