Trig: Solving Equations 3

[Avatar230594]

Somebody failed High school Maths

[megoodok]

you are a university math teacher for sure!

[jesusclau1]

Thank you sooo much for allll your vids. Seriously, I have no words to describe you: you'r just a genius!!!!!!! Thank you.

[bigboycory2]

let (A-50)=X

then now its a chunk problem

then when you get the cosine values then you subsitute A-50 in for x. thats how i would of approached this problem

[ryguy000]

I need ones with period changes ha

[HurdlerBecca01]

Would you be able to solve an equation like this?

3sin θ = √3 cos θ

Where you have to solve for 0 ≤ θ < 360°

And then use the unit circle to find the degree and radian measurement as the answer?

I've been having much trouble with this. ^^;

[TheDunc]

could u divide both sides by (3 cos θ) and get

(sin θ) / (cos θ) = (√3) / (3)

(sin θ) / (cos θ) = tan θ = 1/√3

So think of a right triangle where the not-hypotenuse sides are 1 and √3.

30º, 60º, 90º triangle right?

so which angle, 30º or 60º, should be your reference angle so the opposite side is 1 and the adjacent side is √3? 30º.

30º is also π/6. so there u go.

[sixb40]

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[idius]

In case anyone was wondering how to get the complex values I mentioned in my previous comment:

arcsin(t)=-i*ln(it + sqrt(1-t^2) + 2pi*ik)

where k=0, +/-1, +/-2, +/-3,...

and the natural log of a complex number is the natural log of the magnitude (modulus) of the complex number, r, plus i(theta + 2pi*k) where theta is the phase of the complex number. So for a complex number z,

ln(z) = ln(r) + i(theta + 2pi*k)

once again r=|z|.

[idius]

Of course, in the first part, the solution that was thrown away because it was "too large" is a perfectly good solution. It yields complex values of theta instead of real values. Complex numbers aren't particularly useful at this introductory level, but in general they are quite useful--especially in physics.

Thanks for posting these videos. They have inspired me to make my own instructional videos. I just have to find topics that other people haven't covered well.

[619kammy]

I wish you were my grandpa who lived close by!

<3

[sonnybellows]

thank you mathTV. very clear, precise and simple!

[17Slaves]

Wait?!!! 4-4 = 4??? WHAT THE!!!????

[Baker5874]

oh, haha, never mind, i have no clue why it is 30

[Incuby]

Hehe ^^

[Incuby]

Why is the refrence angle 30°`?

[Baker5874]

That is pi/6. and 45 degrees is pi/4 and so on.

[kdawgg1992]

cuz the cos route3 over 2 is part of the 30 degree or Pi/6 special triagle. ( for Pi/ 6 spec. triangle, opp.= 1 , adj.= route 3 hyp.= 2, cos=adj/hyp therfore cosx= route 3 / 2 which is what were given so we know that that value applies to the special triangle of Pi/ 6 or 30 degrees. :)

[Incuby]

Ahh now i get it.. thanks for the good explanation =)

[1carlento]

thnx a lot sir!!!

[genericvideo1]

awesome! would love to see a video with double and half angle formulas.

[scorcher863]

Thanks sir. you're awesome.

[tholithemba]

yes..the negative sign tells you about the quadrqnts not the value....in that case sin is negative in quadrant 3 and 4....good teacher thanks a lot....i have 1 question though is that the math for university and college?

[MathTV]

I teach it in college, but it is also taught in high school.

[turbold1]

thanks help me alot.. can you do equations on sec and tan? like for example how can you solve sec squared x - 2tanx=4

[nehajohar]

thanx a lot...dis really helps!

[vytautas16c]

Very well explained, thanks

[tomthecool]

Wow, I learn this stuff faster with you than with a "real" teacher!

[bkjoelover]

the best teacher in the world! yipeee

[bobolshevik]

no.