How to evaluate for the composition of two trigonometric functions

👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis.
We can evaluate the composition of a trigonometric function and an inverse trigonometric function using a calculator, the unit circle of the quadrants' triangle. It is important when computing the inverse of a function that the input is within the domain of the function and the output is within the range.
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Organized Videos:
✅ Evaluate Inverse Trigonometric Functions
• Evaluate Inverse Trigo...
✅ Evaluate Inverse Trigonometric Functions with a calculator
• Evaluate Inverse Trigo...
✅ Evaluate Inverse Trigonometric Functions | Learn About
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✅ Evaluate Inverse Trigonometric Functions given a Triangle
• Evaluate Inverse Trigo...
✅ How to Evaluate Inverse Trig Functions without a calculator
• How to Evaluate Invers...
✅ Evaluate a Composition of Inverse Trigonometric Functions
• Evaluate a Composition...
✅ Solve Word Problems in Trigonometry
• Solve Word Problems in...
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[@carmineglitch]

This dude is the best

[@diamondlewis5693]

He literally saves me

[@amasterofone]

I have a trig test in a few days where I'm just supposed to know the unit circle to solve these problems. This is the first time I've seen the unit circle explained this way and I think this will save me. THANK YOU SO MUCH!!!

[@sarahbarah3068]

sharing this to my trig professor bc so many students need your videos right now-- for future reference though could you repeat the student's questions, or list them in the description? thank you so much

[@carolynshaffer8479]

This helped me so much I am literally watching it on repeat! THANK YOU SO MUCH!

[@scubasteve6175]

i hope you at the very least get another million subscribers within 4 years. you deserve so much man

[@Isabelle-ir9iu]

I have been going to tutoring after tutoring with my teacher and she still couldn't help me understand it and you did it in 7 minutes thank you sooooo much!

[@rashmikaabeyrathna1017]

after saw you,i thought one day i want to be a teacher like you..

[@MS-il3ht]

my experience: as long as whatever value (ignore x vs y) you have in the inner-most bracket is in the range out the outer-most function, we can 'cancel'

[@andybob5586]

Great video, great teacher!

[@puneethbheesetty673]

Thank you so much, Sir! if all the math teachers are like you, we students would have colonized Mars by now!

[@wbrady3955]

no we would not have don't be silly.

[@Bob-jj8st]

@@wbrady3955 Ever heard of a joke?

[@insertname5453]

@@Bob-jj8st no

[@jedimasteryoda6309]

Bro you are my hero

[@eswarboss]

Ur explanation is awesome. But u could have mentioned reference angle perfectly as, theta is 45 degrees.. Rather than -45 degrees.

[@ParulBD]

it wouldn't matter as cosine is positive in the 4th quadrant regardless

[@addisonqi8133]

thank you

[@rook839]

Hello. I'd like to ask can we restrict the domain between any other two angles, maybe between -π and 0? If not, could you please explain it to me?

[@joshuaf.pierro9285]

Because going outside that domain interval would cause it to fail the vertical line test, therefore the restrictions are necessary.

[@gabesonawane2227]

can't you just skip to 7pi/4 and THEN restrict the domain (by reflecting) to fit within 0 and pi. Seems way faster.

[@4Jamo]

Do you get the domain from the outer function and the range from the inner function

[@andrewmanzano4792]

I know this is on an old video, but if you made your students voices louder in the videos, I think it would help a lot of us troubleshoot the problems in your lessons even further. Just a thought! I know you're retired though haha

[@haxo1117]

WOW he really teaches the math

[@brianmclogan]

Yes

[@nameholdingplace]

Thank you

[@brianmclogan]

Very welcome!!

[@jessiegustine1486]

What do I do if the x of the function is not a typical point on the unit circle for ex. 11pi/8

[@melissahernandez4329]

i can't find a good video that explains problems like that...im trying to solve one that's 10pi/7 >__>

[@Cheyenneuniverse]

Melissa Hernandez omg Same , so annoying ! And a need it for my test soon. If you find one let me know back here and if I find one I’ll let you know ?

[@wachowski9525]

@@Cheyenneuniverse lol your test is prob over, but in cases like that, they should cancel out (like the cos -1 and cos) because 11pi/8 isn't going to give you a clean point on the unit circle

[@fariharahmani9879]

we don’t deserve to watch this for free thank you

[@lowrain.4798]

knowing how to solve this must be nice. *cries*

[@jjpark2786]

Trig test tmrw and it's the first time I learned that these problems are called compositions. smh

[@joulesabagel9417]

subscribing and sending to my group chat

[@SaintHerald]

IM FAILING MY TEST

[@purvisingh10]

So am I 😭😭😭😭