Trig: Solving Equations 2

[halflife1994]

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

[Avatar230594]

thanks for telling me about k

[megoodok]

you are great sir!! thanxs for the videos



[xxAnakondaxx]

It's amazing! Now, I know much more than before. Thank You!

[ARSENALTHEEDIBLE1234]

This man is brilliant! Although I use the graphs not the quadrant diagram so this is a little confusing for me.

[MsPrincexx]

You are seriously an awesome teacher. Your videos are so helpful. Thanks a lot for your clear explanations!

[jesusclau1]

Thank you for your great videos!!!

[smoorej90]

Ya, this guy saved me. And he looks a lot like Jack's dad.

[Breno06]

This guy is a hero!

[sullivanseven]

He is the father of jack in Lost series, he finally found the job

[hichloecheese]

thank you! very helpful!

[Wuzzi55]

I don't wanna spoil the fun, but...

normally when you write: + (or - ) 360 K,

you would have to define K as an integer, because otherwise one would not know what K is. If we would assume that K is a real number, that statement even falls under false. Sorry for the negative commen.

[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.

[0633767jerishowrulez]

k is any number you choose there for it is true. once you plug in any number of your choice and it is with in the restrictions or else there is no solution. are you trying to question trig which is a vastly researched thing for many years.

[Lasereye360]

He already said this in the first video.

Thanks for the useless comment, bro.

[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 ;)

[bamxbam505]

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

[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

[HurdlerBecca01]

This was really useful thanks! ^^

I have one from my homework though that's stumped me. It's:

4 cos² ϴ + 4 cos ϴ = 3

Where 0 ≤ ϴ < 360°

We're not supposed to use a calculator, and we need to use the unit circle to get the degree for the answer.

I tried to subtract 3 from both side so i got:

4 cos² ϴ + 4 cos ϴ -3 = 0

Then I tried factoring it, but it doesn't seem to work?

[t0myuri]

agreed.

[sailtheseaofcheese]

(2cosϴ - 1)(2coxϴ + 3)

[hirohamaman]

then you set each to zero

2cos@-1=0 to where 2cos@=1 then cos@=1/2 which is 60 degrees

[moosefireplace55]

@HurdlerBecca01 First factor out a 4cos x. You're left with 4cos (cosx +4) = 3 so 4cosx=3 or cosx+4=3 Divide by four on the first one and you get cosx = 3/4. On the second one, subtract 4 and you get -1.On this, you would have to use the calculator and type in cos -1 (.75), which is approximately 41 degrees

[moosefireplace55]

@HurdlerBecca01

Cosine is + in quadrants I and IV, so draw two reference triangles, one in each quadrant. 41 degrees is a solution, and a second solution would be 360-41= 319. Cosine is only negative at 180 degrees for the range given in the problem. So your solutions for the problem would be 41,180, and 319 degrees.

(sorry it was in two parts)

:)

[Koldness99]

god bless you

[krarox]

coool it helped but fix your camera dud technical malfunctions ;;; lol more more

[pogoGIRL33]

i wish you taught my class, I'd have an A maybe.

[brightnessQQ]

i wish you were my teacher.

[SELGX]

thanx sr you are an amazing teacher

[annoyingdude99]

nice vids.... i lost my notebook so i was screwed until i found this video =D

[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!! =)

[washinmachin]

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

[arfanrasul]

Thank you very much for this, really appreciate this!

[xelap11]

awesome

:)thanks for the help!

[pooyoudog]

this is really helpful

thanks matee

[1carlento]

is cos = -1/2

not 120 degree?

[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

[1carlento]

oh i see thnx for that ;)

[kebabrepubliken]

thank you sir! your the best :D

[sharkyboy36]

KEEP IT UP SIR I luv ur videos -_-

[bobolshevik]

Would be better without camera mishaps...

somewhat neat handwriting for someone who masses math videos on youtube..

USE RADIANS, kid

[x4812k]

he DOES use radians.

[alexhmmr]

Better than the original.....