solving a trig equation with the double angle identity (hard one)

Here's a hard trigonometric equation for students who are taking trig or precalculus. We will solve cos(2theta)+6sin^2(theta)=4 (i.e. solve cos(2x)+6sin^2(x)=4) on the interval 0 to 2pi. How do we get all the solutions of a trig equation? This math tutorial will help you be good at solving trig equations!
#precalculus #trigonometry #blackpenredpen

[@davidstokes8147]

I had pretty good teachers of analysis and trigonometry which were my best subjects in maths, yet I can't help wishing I'd had you instead :) I'm 70 years old and use very little maths nowadays but I love watching your videos. I'd love to see something about complex analsysis (although maybe I just haven't encountered those videos yet).

[@blackpenredpen]

Hi David.
Thank you very much for your comment. I am extremely happy nowadays because people are watching my videos and find them helpful/entertaining.
bprp

[@japotillor]

I would have done (sin θ)^2=(1 - cos 2θ)/2 instead of dealing with squares

[@simpletn]

This is apparently the easiest question I ever seen here

[@petachad8463]

This is a question that can come in class 10th board/pre-board lol

[@holyshit922]

cos(2theta)+3(1-cos(2theta))=4
cos(2theta)+3-3cos(2theta)=4
-2cos(2theta)=1
cos(2theta) = -1/2
2theta = 2/3pi+2kpi
2theta = 4/3pi+2kpi
theta = pi/3 + kpi k in Z
theta = 2pi/3 + kpi k in Z

[@gloystar]

At last, I managed to solve something correctly LOL

[@coreyshimashukaa]

your awesome , wish you were my teacher right now hahaha

[@blackpenredpen]

Corey Shimashuka thanks

[@muhetotelance7995]

thanks for your help!

[@junetwenty2835]

Why don't you just use the formulae for that?
If sinx=sin(theta)
Then x= n(pi)+-(1)^n(theta) where n belongs to Z
And formulae for others are there too ?¿??

[@ulquiorra3561]

He was just trying to show different things...I guess

[@dantea6]

Thank you for the background music.

[@nurulfarahaimi8936]

thankyou so much

[@itzshortclipz8016]

i appreciate you.

[@technotux7835]

How can I solve:
sin(2 theta) =0.998
What is theta?

[@RaffaelloLorenzusSayde]

Does it matter which one you use for cos2theta?

[@michlop452]

I know its been a year but yes it matters, you want to completely remove cos(x) terms and keep sin(x) to turn the equation into a simple quadratic, so you use cos(2x)=1-2sin^2(x)

[@neuralwarp]

But you could then have solutions like 7π/3 etc. It would be neater to express the solutions as an infinite set defined parametrically.

[@joshmcdouglas1720]

He defined the solution to be between 0 and 2pi from the start in order not to worry ab this.

[@waldersasytz4274]

Чё так долго это решал, уравнение же легкое

[@jesusriegastorre1205]

+2kphi k integre

[@belmokhtarbentadj9794]

you are amazing
thanks

[@speedspeed121]

Cool video