Evaluating Inverse Trigonometric Functions

[@TheOrganicChemistryTutor]

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[@jinnjinn5567]

*Domain of inverse trig functions* arcsin [-1, 1] arccos [-1, 1] arctan (-∞, ∞) arccsc (-∞, -1] and [1, ∞) arcsec (-∞, -1] and [1, ∞) arccot (-∞, ∞) *Range of inverse trig functions* arcsin [-π/2, π/2] arccos [0, π] arctan (-π/2, π/2) arccsc [-π/2, π/2] arcsec [0, π] arccot (0, π)

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[@Tmzski32]

You should note that tan^-1 does not include the pi/2 or -pi/2 for the range, since you would technically be dividing by a zero which is undefined. Therefore, your range for inverse tan is (pi/2, -pi/2), not [pi/2, -pi2].

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My math teachers handwriting is so bad I cant understand any of the work she is doing online, you’re saving me from failing

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no literally😭

[@jackwang2808]

It's all on the unit circle. My teacher gave my class copies of it and it's very helpful. I suggest printing one out and putting it in your notes if you have them!

[@nyahchristopher3257]

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@@jackwang2808 i dont have to memorize all of that right?

[@ahmedp3]

hello teacher, just making sure, in 11:22 cos 45 is 1 over square root 2, i checked multiple times

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[@brightwolfz]

The explanation for range was extremely helpful. I was confused on what was right and what was wrong when there are two answers that look like they could work, but the automated teaching system my college used just said "That's right because it is!" and I was like "but why though?" Thanks for the vid.

[@nuhanuha5206]

Same here!! Our teachers are like ordinary text books they don't explain more than that oh really sorry they can't even do that also 😜 but u r legend 😎😎😎

[@morganolivianewton8061]

I was so confused, and then you answered my frustration within the first 2 minutes of this video (the arcsin range). THANK YOU!!!! Love your videos.

[@RodahZyambo]

He really knows how to explain.Thank you🙏

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honestly, I'm shocked no one has complemented this guy's voice, i mean the voice itself sets up the mood for studying. You've got a nice voice (if it's a voice filter then also, the way of teaching is excellent)

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[@lorenzogurrola6084]

They threw inverse trig equations at me in ACT Math and I wasn't ready! Your video helped me a lot thank you

[@pablosesaid5830]

is there a video on evaluating inverse trig functions of csc,sec,cot ?

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[@ambasing_omaygot]

Range can't include -pi/2 because it's also one of the horizontal asymptotes of the arctan(x) graph 15:39

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[@aaravshah8839]

Thank you soo much I have a test on this tmrw morning.

[@georgesadler7830]

MR. Organic Chemistry tutor, thank you for a well explained and define lecture on the Evaluation of Inverse Trigonometric Functions. These functions pop up in all areas on Mathematics and Engineering.

[@josephjohnson4761]

My classes textbook did not make this clear so I went home and ate chicken tenders and watched this video and I got it! Thank you a bunch!

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[@sukhbanikaur5543]

At 19:06 would 330 = 11pi/6 count as a correct answer if there are no restrictions

[@ThePennDiesel]

It’s the right point on the unit circle, but it needs to be renamed as a reference angle in order to fit the interval. Does that make sense lol?

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@@ThePennDiesel oh yaaa kinda. Thanks!!

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[@ubbuub]

At 5:16 why can't a possibility be -150 degrees as well?

[@mimijilton5228]

It would be in quadrant 3 as well

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[@c4tac133]

5:50 thank you so much for this, I was stumped on this question 😅

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Dude i literally had a test on this on Thursday and i tried to find a video about it but i couldn't find it😭😭. I'm pretty i failed 😭😭

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F

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I no good luck

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F. Tomorrow is my test, and in the latter half of the unit I spent more time doing homework for other classes than paying attention to this class lol, so this is a last minute study session.

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[@thefirefades]

@@Murk.mp4 huh

[@dodobird809]

why is the range for arcsin -pi/2 to pi/2?

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You’re the best! THANK YOU!!

[@lorenzogurrola6084]

Great video for ACT Math prep!

[@boofenschmirtz]

how do i solve for a function with more than one trig operation in the function. for example, cos(sin^-1(1/2))

[@karenvaldez8014]

Keep order of operations in mind. Evaluate sin^-1(1/2) first...pi/6. Then evaluate cos(pi/6)=sqrt{3}/2.

[@michellewu3050]

sin^1(1/2) is pi/6, then you do cos(pi/6), which is root 3/2

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Whoever disliked this video disappoints me. How does someone explain it so well and you still cant understand it?

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Disappoints? Get a grip; people struggle on topics and especially math. What’s more disappointing is you can’t spare some empathy.

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Seriously a life saver

[@maelfandi3259]

i gotta a question in the example squrare root negative 2 over 2 he gives the angles and is like we already know that the angle of this is so worth. HOW DOES HE KNOW THAT WHERE DOES HE GET THE ANGLE FROM I DONT GET IT PLEASE HELP

[@basraashkir4041]

Plz refer to the unit circle. Type unit circle on KZbin then that's when you'll understand otherwise you'll be confuse. Learn the unit circle first. Good luck

[@Caca10372]

How do you get 5pi/6 in the first example

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This guy is the GOAT

[@savioantony6177]

Thank you man, this was a great help.

[@prodbyKamikaZ]

Arccot(-x) requires you to do tan(1/x)+180 to get to quadrant 2

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Thank you for making these topics sound interesting.

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Lifesaver thanks for the video!

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bro is saving lives here

[@wanguilucie-rs8yk]

How do you identify the range of the angle?

[@penguin2878]

3:15 That was so cute ☺️

[@davidthomas6043]

Although I agree with this and similar lessons, why the fixation on such a small range of angles? Why not 20 degrees, 75 degrees, etc. In all cases, the calculator gives the answers for arcsin between -1 and +1.

[@kaputt_jay3873]

How do you know off the top of your head that pi over 6 and 5pi over 6 are equal to one half? Is there an equation to figure that out, or did you memorize the entire unit circle?

[@fazebugatti988]

memorize the unit circle. our techers made us do it and its really helpful, especially if ur planning on taking calc

[@kaputt_jay3873]

@@fazebugatti988 Yeah, that's what I ended up doing . . . painful, and I already forgot it, but it was worth knowing for the test I took. Thanks.

[@mogethecurator3232]

Came here to figure one thing out. That one thing is the only thing not explained. When and where was I supposed to learn that sin (pi/6) = 1/2? Typing it into a calculator doesn't give 1/2. The unit circle only deals in radians and degrees, so that doesn't do much to equate radians to fractions either.

[@basraashkir4041]

Plz refer to the unit circle. Type unit circle on KZbin then that's when you'll understand otherwise you'll be confuse. Learn the unit circle first. Good luck

[@squadofone7170]

EXACTLY THIS!

[@squadofone7170]

I don’t understand SIN is opposite / hypotenuse so why is he saying it’s only the height (just opposite?)

[@nanouk218]

Is there a typo at time “8:39” Cos(5pi/3)= sqrt3/2 right?

[@leanne4619]

No