Trig: Solving Equations 2

This mini lecture appears in Trigonometry, published by XYZ Textbooks. The video appears in the eBook and is also accessible through one of the QR codes in Chapter 6 of the printed book. Access to all the eBooks at XYZ Textbooks is $45 per year. The print book sells for $50 and includes access to all the eBooks for a year. There are over 700 instructional videos embedded into the eBook, and more are added each year.

[@sabrinamorales7646]

My teacher is extremely smart, but he doesn't know how to dumb things down for the class. He's also very vague and expects us to know everything he's saying without showing things on the board. But not this guy. He's very clear about how and when to do things. I'm definitely subscribing. This channel is officially my new online math tutor.

[@894Time]

You are a wonderful person for making this. Helps me out a lot more than my class's explanation did!

[@proteopathy]

Such a brilliant teacher. Thank you for sharing your gift with the rest of us.

[@Kamzui]

OMG You are like God! I was really scared about going to fail my IB Maths Standard Level examinations since I understood absolutely nothing in my maths lessons at school. But you make it all very VERY easy! I love your videos!! =)

[@fiftydowabill]

you find it using the trig inverse buttons on a calculator, or with triangles if you have special angles of 30, 45, or 60

[@gerardmatar]

May I just say that i Love you. I have my honors trig final tomorrow and I have never been more clear on this subject than I am now.

[@sunshine-bj8ih]

You are the best! Thank you. I can work this problems without having to struggle with unit circle

[@abrown5526]

Another great video. Thanks.

[@Un1ted-Kingdom]

Hi sir why do you add 360 degrees to the values to find out all the rest of the angles..??? It's this ONE THING that i don't get why also my teacher does this?? :) ur great help

[@wombocombo6878]

There are two places where cos= -0.5 one is 120 degrees the other is 240 degrees, if you put cos 240 in deg mode, you will get -0.5

[@mkayzondy]

very helpful...thank you

[@TheStarfish13]

THANK YOU JOHN LITHGOW!!!

[@nanosanchezlopez575]

Arcos of -1/2 is 60 degrees? :( I thought we had to apply what quadrant it is positive in? 60 degrees is in quadrant 1, where cos is 1/2; cos60 in quadrant 1 is 1/2 not -1/2???? :( Please answer??

[@herbalist0]

this guy is my hero! i want to hug him!

[@Kamzui]

Yes it is, but if you don't have a calculator you will first need to find out what cos= 1/2 is, which is 60°. At the end he shows us that all solutions for cos=-1/2 is 120+360K or 240+360k

[@punjabi555forever]

why are the answers in radians for one and in degrees for the other?

[@starcalibre]

yeah, N would really be a better variable to use if anyone wants to use Mr. McKeagues otherwise valid methods as this implies the set of natural numbers.

[@yippyyay]

I don't understand how you find the reference angle =(

[@corbinfisher5703]

Thanks, Super helpful

[@TRAPPICK]

i wanna ask that one too, i tried checking it with my calculator and it says 120...

[@zcruz123]

do some with tangent

[@AmzSongwriter007]

Your method would not work as you cannot use the zero product property.
It does actually factor out into (2cos ϴ-1)(2cos ϴ+3). You would get cos ϴ=1/2, and you reference angle would be 60°, or cos ϴ=-3/2 which is not between -1 and 1 so that part would have no solutions.

[@dohafaeq711]

شكرا شرحك حلو 😍

[@freedomisjoy]

Thanks for the help!

[@hichloecheese]

thank you! very helpful!

[@1carlento]

is cos = -1/2
not 120 degree?

[@kebabrepubliken]

thank you sir! your the best :D

[@Blueknightex]

I don't get it how he got a 60° from
x=cos-1 (-1/2), I got a 120°....

[@Blueknightex]

I get it now. cosx=1/2 is 60° right? but
there's minus(-) sign in front of 1/2 so it is counted as a negative 60° which is why
Sir, here drew the 60° graph on the left side because it is a negative. Try not to confuse yourself with a calculator thinking that it is 120° because that shows that you don't have a clear understanding of trigonometry. It's all about knowledge and common sense ;)

[@Dominator32RW]

Thank You!

[@danemueller756]

thank you. this video gave me an epiphany

[@halflife1994]

cos = -1/2 is tangent 60 degrees??????? i think its 120 degrees

[@nanosanchezlopez575]

Please make more videos! :(

[@IIOsOsII]

isnt Cos-1(-0.50) = 120? im sure it is

[@radilfio]

Why doesn't he just use the unit circle?

[@908bruhh]

you do it when you have to find all the available solutions.
i.e. 2piN

[@TheChewymac3]

Thanks

[@matokurin]

Great

[@x4812k]

he DOES use radians.

[@brightnessQQ]

i wish you were my teacher.

[@Koldness99]

god bless you

[@t0myuri]

agreed.

[@watts-jake]

I love the apology...

[@1carlento]

oh i see thnx for that ;)

[@washinmachin]

so apparently i didnt do that well on my test...

[@nanosanchezlopez575]

Nvm, I should have kept watching :D

[@tonianev]

Mmmmmm pie

[@nanosanchezlopez575]

:)

[@user-dr2xt1en6u]

talu

[@fyhatters]

pendong!