How to find the reference angle | 16 Examples 

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I’m 35 taking pre-calculus for the first time and before I discovered your videos, I’d spent many nights between tears of confusion and maniacal laughter…also in confusion. You are a Godsend, thank you! Edit: #13 was what I was stuck on. They gave us the answers for review, but I just didn’t get the process of how they got pi/6 as the reference angle. I get it now!☺️

I always come to your channel to find a specific answer to a question I have that my teacher didn’t cover in class and you always have the perfect answers that are easy to understand! Too bad RU-vid doesn’t give away teacher of the year because you’d definitely win!

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this video literally saved me from my finals

As a high school Precalc teacher, I'm interested to know what software you use to create your videos, including the whiteboard feature. You make it look so simple!

Thanks man I’m so happy you still make these. You help me so much with math and I can’t express your help. Thanks again

I just wanna say thank you!

Thanks for this video. It really cleared all my doubts

It was posted 1 year ago and here I am watching,thank you for all the knowledge

Thanks to you, this really helped me because I have troubles with trigonometry and our math teacher is terrible...

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Thank god someone has more than one example.

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Nice. Love your videos. Super clear and precise. I might be getting ahead of you here. I should probably look at subsequent vids. From a more intuitive and visual standpoint, I see the reference angle as the angle in Q1 whose coordinates you would use to determine the coordinates of any angle on the unit circle that is a multiple of the reference angle (and therefore the cosine and sine values of those angles). It's about symmetry. For example, if you have 120 degrees, the the angle most useful to you in determining the coordinates at that point around the circle is 60 degrees. Its directly opposite 120 in Q1 (symmetry wrt Y axis), and therefore the x coordinate (cosine) will be negative, and the second (sone) will be positive. The big idea is that by remembering the coordinates of angles in q1 for 30, 45, 60 degrees (although in reality you only need to remember 30 and 45), you can determine the coordinates of any angle on the unit circle that are multiples of 30, 45 and 60 via the multi-symmetrical nature of circles. Also..if you are given the, say, the sine of 37 degrees (0.0602), you can still use the concept to determine sin 143 degrees (-0.602). etc etc. Get used to quickly sketching the unit circle if you are visual learner. Ultimately, you don't use the term reference angle when you do calculus - it's a strategy to help you understand how use the unit circle to find trig function values, but most importantly to help you learn how to determine inverse trig function values. ie. the angle, (or time, for example in application problems) given a trig function value and a quadrant.

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Your a lifesaver Brian, Thanks for all the amazing lessons

Very fantastic explanation teacher! Am very happy, cause you made it easier that I understand it immediatly in this video. Am really glad About that.. thanks

Many thanks for this awesome video. Very interesting that you mentioned that clockwise or counterclockwise is not an issue when we're talking about reference angles and its just the scalar value of the positive acute angle which is important. At the beginning, before watching these videos I had checked several tutorials on the Web with figures indicating a reference angle with positive value yet with a clockwise orientation and I was confused that why the angle is being written as a positive. Many thanks!

Yet again this guy can teach what my teacher cannoy

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Did you ever make a follow up video for how to use reference angles in functions? Thanks for any info.

Sir, thank you. I’ve spent all day trying to figure out a smart way to locate radians without having to completely “memorize” the unit circle.

your videos really help me alot !!!

this helped me so much, thank you!

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Thank you so much for all your videos

Thank you very much

It 2 years ago and it so help full

Thanks for this as I didn’t understand before :)

Awesome I did understand it❤❤

Thanks lot of help to the online learners

Thanks so much! This helped me alotttt!

I do like this format better where your explaining only to the camera and not the normal teaching to the classroom setting.

Your videos helped me pass my exam today 🙏🏻

You are life saver thankyou👍

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thank you, i have an exam & im studying last minute but at least i know how to find the reference angle now :s

this is really helpful, but i am not quite getting to grips with 15 angle (5pi/8)

This is very helpful for me😭❤️

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The Goat!

What I can't figure out is how to find a reference angle of 14pi/9 I know it is bigger than 2pi but how do I figure out the coterminal angle with a radian that big?

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How do i find reference angles given two points on a graph while also not being given the entire angle?

What about having .5 in a given angle ser?

Can you plis teach rational functions graphs

why is it that for 3 and 4 he solves by using degree he is short on but on 2 he uses what he reached?

When he said reference angles were just the distance to the x-axis, everything just clicked.

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I really don't understand the last part :((( and it's finals tomorrow.

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Thank you so much 💝