Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities

Now that we know what these trigonometric functions are, how do they relate to one another? In a variety of ways, in fact! There are lots of identities we will have to learn so that we can do algebra with trig functions later, so let's learn these now.
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[@ryanjamesfuentesconiendo4999]

thanks prof dave.. you saved my 1 semester of math analysis
More power & GOD BLESS YOU MORE

[@shygirl8376]

Just exactly what I was looking for. Thanks you’re the nicest Dave I know

[@zoeig6601]

did a dave break your heart or sumn

[@CJCREATIONS001]

Please do, they're great, this is my first time watching you(apart from brady's videos), and out of all the videos I watched(because I had difficulty accepting it) yours was THE BEST, even better than MITOCW.

[@kosikosi8788]

bvguhj

[@Aristos_Arete]

I appreciate your content, I love to learn so this is a treat for me.

[@uchechukwuntinuokwu5548]

Thank you sir. You just made my understanding of trigonometric identities a lot better.

[@falia30]

Thanks so much for this video! i really appreciate the part where you derive the other pythagorean identities from that one identity. Our prof never really discussed the connection between the trigo identities so it was quite difficult to comprehend the need for these stuff to me but then I came across this vid so they made so MUCH sense now and it really helped me alot :))

[@sarafeliciano3088]

Hi Dave! Decided to go back to university after 10 years...not studying math lol thanks for the super easy refresh! best!

[@studyaccount017]

came here because i misclicked from graphing functions, stayed for the pythagorean identity derivations. if this was how it was taught to me in 8th grade, i would've liked maths a bit.

[@uchechukwuntinuokwu5548]

To be very honest, if I were to have been taught like this, I doubt if I would even be coming to look for channels like his to learn it again.

[@IronEducation]

Thank you so much for this!!!

[@kajalroy5708]

Thank you

[@Attalla-t9b]

This video is gold

[@abdelrahmanhashimmousa9944]

Dude, you're a life saver

[@fthitekle9354]

Thanks

[@hornet-e9g]

thanks prof dave

[@honda.civiccalasiao4643]

Very NICE.....Thank you.....

[@mdsaidulislam8791]

Very good.

[@jahnnagweys]

Thank you so much!

[@tGoldenPhoenix]

Done.

[@crazyjester993]

3:48 sin 30 = cos 90 -30 (because of unit circle theorem)

[@MiltosPol-qn3zh]

Tan · Cot = 1 ?????

[@ProfessorDaveExplains]

yes! sines and cosines cancel.

[@connorconnor2421]

x * 1/x = 1.
Sec * Csc = 1 and Sin * Cos = 1 too.

[@abdullahbinsaad2470]

anything multiplied by it's reciprocal gives 1

[@Alex-02]

⁠​⁠​⁠@@connorconnor2421 Incorrect, I think what you meant was this:
Sin * Csc = 1 and Cos * Sec = 1

[@shahzaibali4337]

hi sir i want to clear my problems about cofunctions can you explain with example

[@siyarama21]

No

[@taimulahmedjisan3590]

Thank you sir🇧🇩🇧🇩❤

[@rohitrajhans6510]

Very thnx

[@deepanitin1684]

sir how do u obtain cofunction identitis for 270+x etc..

[@mibit2720]

Awesome

[@duniamachado4669]

U r smart

[@connorconnor2421]

biggusbrainus

[@joschaberg6940]

Addressing Cofunction Identities:
Why do we define them as e.g.
sin(θ) = cos(90° - θ)
when we could also write:
sin(θ) = cos(θ ± 90°)
?
I assume direction to which we shift the angle does not matter als long as we shift for exactly 90°.

[@azaria2977]

because it doesn't always work in addition. for example sin(90) does not equal cos(180°). addition works for certain quadrants of certain functions

[@joschaberg6940]

@@azaria2977 you are right. i was thinking in terms of magnitude solely. thank you.

[@azaria2977]

@@joschaberg6940 you can look at it in graphical terms. it can make it way more intuitive, play with the sine and cosine graphs in desomos.

[@fruta6279]

The Confusion Identities

[@izanovavery]

Nice one! haha

[@littleretroship6403]

If (sin θ)²+(cos θ)²=1, then does sqrt((sin θ)²+(cos θ)²)=(sin θ)²+(cos θ)² because sqrt(1)=1?

[@ytfutureCEO]

Yes , you just expanded the RHS

[@avarius3361]

Wait . What grade do they teach this?

[@ProfessorDaveExplains]

Usually 11th.

[@slickyy21]

They taught us this in 10th,strange isn't it?

[@lorekeeper685]

Mew?

[@connorconnor2421]

2

[@Alex-02]

I never understood why in the US they always teach students secant, cosecant and cotangent. I feel like they are never really that useful for more advanced topics and just add more confusion for students just learning about them.

[@lauracarroll3276]

Howdy🎉

[@masterwong8820]

i am the first to comment

[@techgod4284]

Master Wong no your not

[@AJ-gx8mb]

ur parents must be very proud

[@kosikosi8788]

so much

[@lotkuuu7712]

math jesus

[@nonorv3095]

Oh no. Why the answers are not explained? 😭 sooooooooooo sad!!!

[@ProfessorDaveExplains]

in checking comprehension? there's nothing to explain, they are simply the identities that are listed in the tutorial.

[@sristisingh03]

arr sir ji Indian bn ke padhao yaar.... hmlog Indian h... okk

[@navjotsingh2251]

Ji ye ladka angrezi hai, hindi nahi aata hai kio ke vo american hai.

[@vasu2415]

Thanks