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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[@jn4198]

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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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[@Agoobernamedseth]

This really helped me with double angles, thank you so much 🙏

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

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

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

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[@jamesfay6234]

@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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3:54 how did you get the 4?

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

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[@mocha---]

cos(2x) = 2cosx-2sinx

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Dead

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[@mocha---]

sin(x+y) = sinxcosy + sinycosx

[@mocha---]

sin(2x) = 2sinxcosx

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Our teacher asked us to work the problem out in bold on paper and hold it up. I scribbled organic chemistry tutor as legible as possible and held it up.

[@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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[@jaychoro8159]

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

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[@liwiikiwii]

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

[@Buddhabebop]

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

[@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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thank youuuuu

[@QuangNguyen-dw9je]

0:07 No I don't remember that equation

[@AmberRathour366]

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

[@supremechair5812]

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

[@jrzzyplayz8692]

Is this further maths only

[@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.

[@qquamau7]

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

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Yea i need to know too

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how do i do stuff like cos112.5 in angles?

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[@Rose-hq5zk]

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

[@tabiosmariojr.6412]

what if the question is secant, cosecant and cotangent

[@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.

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the best

[@mikengaaisha3187]

Sir so not understood where the 4 comes from