Solving Trigonometric Equations

Solving Trigonometric Equations - Step-by-Step Examples
In this video, we explore how to solve various trigonometric equations using different techniques. We'll cover multiple example problems, each demonstrating a different type of trigonometric equation and the methods you can use to find solutions. Perfect for students wanting to build confidence in solving trigonometric equations and understanding their applications.
What You Will Learn
How to solve linear trigonometric equations like 2cosx−1=0.
Techniques for solving equations involving trigonometric identities, such as sin(2x)=cosx.
How to handle more complex equations like 2+cos(2x)=3cosx.
Strategies for solving equations involving multiple trigonometric functions, like sinx=tanx.
Solving trigonometric equations is an essential skill in algebra and trigonometry, requiring a mix of algebraic manipulation and trigonometric identities. By the end of this video, you'll be familiar with various techniques for approaching these equations, including factoring, using identities, and isolating trigonometric functions.
If this video helps you understand how to solve trigonometric equations, please like, comment, and subscribe! Share it with classmates, teachers, or anyone learning trigonometry.
Support my work on Patreon: www.patreon.co...
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[@worldzfire]

You are a brave man doing trig in sharpie

[@Scrappycamacho19]

haha at least we know our tutor is confident

[@hollyjo161821]

I just got to say, I sat in class for two hours with my Trig professor, and I learned more in 10minutes from you than him. Thank you sooo soooo soooo soooo much!!!!!!!!!

[@patrickjmt]

+Holly Robertson happy to help, come back any time!

[@israelt1764]

same

[@patrickjmt]

@PaperNotes at one point, google automatically put ads in the middle of longer videos, i am trying to remove them all. and once again, this is why youtube is free for people: the ads. there are many websites where you can pay a subscription and not have to watch any ads if that is what you prefer. go forth, and use them.

[@CerebralSnake]

Man, I never bother to sign in to my account much just to post a comment, but my gosh you are seriously a life saver. You fed me more knowledge than my trig teacher did this whole semester. People like you just take loads of stress of others and there need to be more people like you in this world. Thanks so much man. It's really appreciated. :DDDD

[@accolade37]

Thankyou so much for your videos. I find them really easy to follow, you go slow enough and explain things clearly so that it is easy to understand your solutions. I have watched many of your math videos and have found them very helpful. My students like them too!

[@patrickjmt]

glad it helped! make sure you know some trig identities, or these problems are really hard otherwise! : )

[@superhume]

your my hero. You just taught me what my teacher has been trying to do for two weeks. Thanks a ton man.

[@Mustang5Speed]

I love Math but trig has always been tricky for me. You sir are the best reference so far. Thank you!

[@KruspeFTW]

Thank you so much for your help. I was absent from class when we went over this, and self-teaching wasn't working so well.

[@ryanfacks1717]

This helped me very much with my precalc/trig class on a certain lesson. Thank you!!

[@patrickjmt]

no problem, happy to help! i have a video about how i remember all the values on the unit circle if it helps...

[@yvr6]

One thing's for sure, you explain this way better than my math teacher! Thanks a lot, now I know what I'm doing.

[@rojulideckor]

You are really the only reason i'm understanding anything going on in my math class at the moment. THANK YOU SO MUCH!!!!!!!!!!!!!!!!

[@jwong2332]

Hey man thanks for making all these videos theyre extremely helpful and youre a much better teacher than my teacher

[@Ohmz27]

Yes, its in college courses for A-Level maths. The exam board im doing it with has this stuff in the C2 paper.

[@patrickjmt]

@Nasirkg2 glad i could help. hang in there! i think i have a trigonometry playlist on here...

[@patrickjmt]

@creeper569 i had an opportunity to take that, but didn't. not sure what you need; best thing is to watch videos! i have a trig playlist if it helps

[@DarkSasori1]

That was great! :O Your video will be of great help for my graduation exams at monday :D

[@patrickjmt]

@Mustang5Speed glad to help!

[@blkchrm77]

i used to think this was the hardest part in math class. i even asked my teacher for helped and it kinda helped but i still didnt fully understand, plus he goes too fast. but now this stuff is easy. THANK YOU SO MUCH!!!!

[@Pigsbum53ASMR]

you are so much better than my maths teacher thank god for youtube and you right??

[@RedTriangle53]

For anyone who doesn't get the fractions with pi that he translates the trig values into, they are called radians and represent angles. In essence, since pi=diameter/circumference, pi will always show you how many times that circle's specific diameter is wrapped around it's circumference. That's why 2pi = 360 degrees. Any angle between 2pi radians and 0 radians can be expressed by fractions using pi. So a straight angle(half circle), (360/2) degrees=2pi/2, is equal to pi radians, and a right angle(quarter circle), 2pi/4 is equal to pi/2 radians. So it's a shortening of a ratio between your selected angle, and the full circle. it always follows the rule of 2pi over how much of the hypothetical 360 degrees your angle consists of, so 60 degrees = (360/6) degrees= 2pi/6 = pi/3, and so on.

[@sorekaru]

Pretty sure it's circumference/diameter.

[@RedTriangle53]

indeed it is. I stand corrected.

[@edchiladas]

I thank you for the easy to understand video of solving trig equations! I have a big test tomorrow and these will be covered. Thanks again

[@patrickjmt]

@Lingox5 cause that is how people decided to define it

[@patrickjmt]

no problem : ) glad to help

[@Zacboy95]

If only there were more teachers who taught like you... thank you so much

[@619kammy]

6sin30X-3=0 sin30x=1/2 x=30 or 180-30=150 sin x= 30/30 or 150/30=5 x=1 x=5 Now what is the period here to add in order to find the solutions? 0

[@maximillianortego4737]

the topic(Trigonometry) was new to me back then so i had to use you tube to aid me in my studies because my math teacher isn't really good at explaining. thank you for your explanation but i already know

[@krazycrarie]

Man, your rectangles are freaking neat. How do you make straight lines without hesitation gaaahh!! Thanks for all the math help!

[@lovingislifeviv]

love your math videos! especially cause i have a trig test tomorrow haha

[@megsXoXoXo]

I almost started crying during the trig equations in class because I had no idea what to do. My next test is tomorrow, and I feel a hell of a lot more confident. Thank you so much you mathtermind

[@kristenkarcz]

You are a lifesaver !! I've been struggling to figure this out for the past week and I finally understand it!

[@SuzakuHayasora]

Thank you so much! This is really helping me for my summer math!

[@219thomas]

This is very helpful, I enjoyed the way you explain your solutions.

[@hassanouanir6107]

Nice Patrick, I like the way you do trigonometric problems It's the same way I do it back in the days so these stuff is a nice reminder for me thnx a bunch

[@headphonezombie]

Patrick, you're my new hero. This has helped me in 10 minutes way more than my tutor has... haha maybe I won't fail my precalc final today

[@adamczasak5866]

Very useful and professional. Easy to follow. Thanks

[@TheInsidious21]

Is it bad that I absorbed more about the unit circle from this 10 minute video than I did from 1-2 months of the unit circle in my actual class? Great Vid Patrick, thanks for the help.

[@tobiastobyburns]

patrickJMT, your videos are the best. You crush it.

[@patrickjmt]

@mclarenmc88 oh, ops, get an A* then. what do i get if you do not make an A*?

[@MrTopperAZ]

you sir have saved my life! You deserve the teacher of the year award.

[@BlazedOutTurtle]

The first example he did, was the first problem on my homework, Thanks PatrickJMT !

[@patrickjmt]

no problem

[@rhorbat]

Before factoring the 2Cos^2x-3Cosx+1, arent u supposed to multiply the 2 in front by the 1 in the back, so then u get Cos^2x-3Cosx+2. And after factoring this, you should get (2Cosx-1)(2Cosx-2)?

[@EmmyG954]

OMG!!! Thanks man I really was dying in this Trig topic(s) because I couldn't understand my teacher, and still can't but with you I understand you all the way bro. Thanks Alot. I really appreciate it.!!!

[@katherineandblair]

....I'm pretty sure that you are going to be the sole reason that I pass my math exam. GOD BLESS YOU

[@mohammedraza8417]

U have the right side correct but the LHS of the equation is suppose to be sin(2x). If u use the double-angle formula, sin(x+x) = sinxcosx + sinxcosx, which further simplifies to: sin(2x) = 2sinxcosx. Hope that helps :)

[@xoxoChristiina]

you're fabulous. but I'm still dropping math after calculus AB junior year, despite this having been extremely helpful in improving my understanding of trig equations. Thank you!

[@honey123401]

You are my sunshine .. my only sunshine ... u make me happy when trig blow my mind away!! Thank you so much dude..

[@QuietGuitaristfan]

I basically just needed to see more examples of factoring because my teacher only showed us those easy ones from the book. Thanks

[@TheRoldmeister]

Thank you, patrickJMT, I have seen the light thanks to your teaching

[@iamargenn]

this actually helped me! i have a project in math and i have to pass it tomorrow! THANK YOU SO MUCH!!! ^^

[@dharding5692]

Thanks a lot this really helped for my pre-calc test tomorrow!

[@619kammy]

We are using "HL Maths for the IB Diploma"We have equations like the first one you showed, maybe more complicated. I was wondering. When you have found the two solutions to an equations, and now need to find the rest withing the domain like 0

[@patrickjmt]

thanks!

[@maximillianortego4737]

thanks about saying the part 3:50 -3:55 my teacher didn't explain why removing or canceling a trig function to one will make me lose a solution... he just keep solving and solving and let us copy his work without the actual explanations

[@lovisahagstrom]

DUDE YOU ARE AMAZING, IVE BEEN TRYING TO FIGURE THIS OUT FOR MONTHS AND I FINALLY GET IT. THANK YOUUUUUUUUUUUUUUUUUU

[@fafase]

@Yinkaldinho 2x^2-3x+1 let's say they are a,b and c you do: a times c 2*1=2 then find 2 numbers that when multiply give 2 and added give-3: -1,-2 in this case, then decompose b (-3x) into those numbers: 2x^2-2x -1x+1, then organize in 2 groups and find the GCF: 2x(x-1)-1(x-1)Both factor groups should be the same (x-1) in this case.your GMF's are one group and the factor groups are the 2nd group:(2x-1)(x-1).=>(2cosx-1)(cosx-1) He seems to do it in his mind, I can't. Hope you understand now.

[@AlexK9465]

Getting ready for my Pre Cal 2 final exam. These videos are helping a lot.

[@SjCerealkillers]

PreCal finals tomorrow&ready to rock. You're the best

[@XwP1ayawX]

Dude, that just helped me a bunch. This is awesome.

[@skrevat]

its not that my teacher is bad, it's just that you're so damned good. if i question any part of my math, i just look for your videos and refresh myself with what you have to say. you better be making money off this.

[@OriginLegend]

This was such a HUGE help. Thanks!!!

[@thespartanchannel]

These videos are wonderful. THANK YOU

[@patrickjmt]

no problem : )

[@gene546]

Thanks man for your contribution to education.

[@iikamuii]

Ok it's starting to click to me now. I'm slowly starting to understand this better. Thank you kind sir.

[@patrickjmt]

@Xmaggot93X glad to help you maggie!

[@Iamorton]

you should get payed for this man..because my math teacher isn't so useful right now

[@geetar1226]

your, "using the unit circle with the coordinates of the point being (cos, sin)" thing isn't wrong by any means, but doesn't help much when dealing with the Tan function. It's a lot more useful and self-sufficient to just memorize the special triangles and use them as a reference, and save the (cos, sin) deal for just if your angle falls on an axis, (or more specifically when the values of the function are 0,1, or -1 for sin and cos funtions or 0 for tan)

[@Bowenarro111]

This was really helpful, thanks for uploading!

[@netanelgichtin2772]

you can divide by cos x if you check to make sure it won't eqauel 0

[@gmt3gmt3]

thank you i was really stuck on this it really helped alot

[@MrMaxileahy]

Thankyou very much! This was exactly the help i needed :)

[@losebiramnickove]

Give this man a medal, I'll get him beer. He deserved it!

[@charleswilson7789]

Thank you so much for posting these videos! I've gotten so much help and I really appreciate it!

[@arstgkneio]

can you do an example where you have to signify all solutions to the trig equation using the variable k = any integer?

[@MrChesster7]

you are a life saver, thanks bro!

[@619kammy]

I have a math test on this tomorrow..or technically today. Down side: We dont get to use a unit circle or anything on the test so we have to memorize. In the other hand i have the memorized the sin/cos/tan table from 0-210 degrees. Well Im gonna check back with you later. Good job btw

[@bitty88]

This helped so much....I love you.

[@BobbySims]

Hello Sir. Thank you immensely for the videos, they are tremendous. I have an area I'd like to see you cover. I've been asked in homework to "Write the expression below as an equivalent expression involving only x. (Assume x is positive.)" The expression is tan(sin^-1(x)). The class only lasts another week. It's a 5 week course and trying to learn this in 5 weeks has killed me almost. Any help would be appreciated. Thanks, brs

[@RahulKeswani84]

your final answer should always indicate an integer multiple of the solution like (n+1/2)*pi

[@sukimroxs]

For the question "2+ cos 2x = 3cos x" what happens to the 2+ when the equation becomes "2 cos ^2x + 1= 3cos x" (8:26)

[@gebreigziabher3008]

Hi there. Patrick missed a step here, so... when he applied the trig identities to 2 + cosx = 3cosx, he ended up with 2 + (2cos^2 (x) -1) = 3cosx.....so the next step is where he skipped....if you just foil the bracket you would just end up with 2 + 2cos^2 (x) -1 = 3cosx, now if you collect like terms on the left hand side, the 2+ -1= +1 therefore 2cos^2 (x) +1 = 3cosx . I hope that made sense to you. Good luck :)

[@bernardcruz809]

Thank you so much. been looking for this kind of problem

[@bootheb]

This made trig equations so much easier--thanks!

[@MrTrumpetguy25]

Patrick -- Thank you. I was stuck on this concept for the last two days and was about to throw my computer out the window.

[@LLL10719]

This helped a whole lot! Thanks :)

[@ryanholland7101]

It is only true for this specific problem, because we're given sin(2x)=cosx, and 2sinxcosx=sin(2x) is a general trig identity, into which we plug cosx for sin(2x).

[@ITIonoxide]

Thanks man. Helped.

[@Rmadridista4life]

Thank you Patrick JMT! I wish you were my personal tutor but I live in Canada lol

[@patrickjmt]

@RoMaL0 i have videos on this. do a search on my channel of ' unit circle ', there are a few videos on it.

[@patrickjmt]

happy to help :)

[@patrickjmt]

well, no matter what, i am glad i could help you :)

[@letslearnfiziks]

thanks patrickJMT ,you are making me to love math

[@patrickjmt]

Excellent!

[@hellyabro123]

how do we find the trig identities do we have to memorize it or can we take a table of trig identities to the exam ? btw your videos are the best helps me alot

[@candygir87528]

are u like a teacher or something? haha. ur a beast!! it's like u know the perfect way to explain things to ppl that's trying to learn (like me). for some reasons, teachers in school cant. hmmm

[@MahmoudMohamed-fb4wr]

Thanks for your help

[@jmartr34]

@Sumaiya23able All he did was remove the parentheses around the 2cos^2x and moved the 2cos^2 x in front and subtracted (2-1)=1. To sum it all up, he basically re-arranged the terms and subrtracted.

[@patrickjmt]

i think most people are used to using degrees as well. however in calculus, there convention is that angles are measured in radians (no matter what country you are in), so you have to learn to use them. using calculators too much has ruined the mat ability of countless people! i recommend throwing them away!!!

[@2punchforever]

@DillyDally26 its a double angle identity just like a pythagorean identity