Trigonometric Equations Multiple Angles All Solutions

I continue my examples of solving algebraic equations that involve multiple angles such as sin(2x).

[profrobbob]

Thank you for watching...and starting to let me know there might have been a problem. Working full time and trying to make these videos means sometimes I do need a little help from my viewers. THANKS FOR WATCHING:) I hope you do great in your class and please help me by spreading the word about my channel to your friends.

[georgesadler]

Professor RobBob, thank you for Analyzing and Solving Trigonometric Equations with Multiple Angles that has All Solutions. I understand these problems from repetition over time and also using the Unit Circle.

[profrobbob]

I have not finished the problem to check your answer, but you will need to finish with the quadratic formula since it does not factor. You can temporarily let u=sin(3x) to simplify how the equation looks and then plug sin back in after you finish the quadratic formula.

[lukemartin]

Thank you so much for passing on the knowledge.  I'm taking a brutal 6 week pre cal class and thanks to you I can study at 1:00am.  :)

[profrobbob]

Yes...for Sine, Cosine, Secant, Cosecant. Remember though the standard period for Tangent and Cotangent is only Pi not 2Pi

[profrobbob]

If you write tan(3x) as sin(3x)/cos(3x), you can multiply both sides by cos. (cos(3x))^2 can be written as 1-(sin(3x))^2 and then set the equation equal to zero. Now you have a quadratic equation with only one trig function (one variable)

[ogscheidt]

For the second problem, why wouldn't you add 2 pi to your degree measures before dividing? Why did you add pi n to it?

[erwinjedracho]

ohh what a day...i ve watched ur videos from verifying up to this...our finals is over and i know failed but i still watch this cuz i know that learning is much more important than passing..i wish that i would someday undertsand this..tnx btw

[profrobbob]

I think the videos you want to watch is Trigonometric Equations Single Angle 0 to 2Pi Restriction and/or Single Angle Trigonometric Equations All Solutions. The solutions to your equation are 0, pi, .3398, and 2.8. There are two angles where sinx is 0, 0 and pi, and two angles where sin(theta) = 1/3...one angle is in quadrant I that you get from your calculator .3398 and quadrant II pi - .3398 or 2.8

[fcusNa]

Thanks, please keep up the amazing videos! They are extremely helpful! Many Thanks! 

[profrobbob]

Can you be more specific? Are you referring to the +-(period)n to describe all possible solutions or finding solutions around the unit circle that have the same reference angle? Is there a time point in the video when I confused you?

[haamidadam]

@ProfRobBob, i'm a little confused on the the expression we add on the end, the pi n or 2pi n etc. My question is, how do know when to add on +/- because sometimes i see only a +pi n and sometimes a +/- Pi n and sometimes a -Pi n. I know i've not worded this very well but if you could help, i'd be very grateful! Thank you

[profrobbob]

You're welcome soooo And thank you too for subscribing! The growth of my channel depends on subscriber support like yours...please share my channel with your friends:D....thanks.

[myrandaolsen]

no there wasn't anything in the video that confused me i ws just working on a problem: 3sin^2x - sinx =0 and i got he answers 0 and 0.3, but, the answer says to do x= pi - 2.8. Why pi subtract something? or when do you get something like 215 - pi(n). this is to find the equation

[MakeUpRocks]

your students are so lucky to have you as their teacher!!

[jasonelliott]

thanks so much, such an excellent teacher.

[matusz]

Is is safe to say that whenever there's a half angle in the equation, the period will be 4pi, and when there's a double angle, the period will be pi?

[jadenataylor]

Could you do a video with examples of csc and sec? Unless you already have a video about this, and I haven't found it yet.

[Lyssisx]

Do you need to memorize all the values on the left side?

[SheSedSheSed]

how do you know if u add or subtract the pi or 2pi?