sin(3x) in terms of sin(x)

We will write sin(3x) in terms of sin(x). This math tutorial is suitable for trigonometry, precalculus and calculus students.

[KasabianFan]

You need to change the name of your channel to blackpenredpenbluepen

[abijahzimmerman]

yo my teacher spent 10 minutes explaining this in a video and I did not understand it at all. then I randomly found your video. thank you so much!!

[giangtruong]

thank you finally i can understand the reason why

[intuitiveclass]

This is an awesome explanation, thank you man

[MrJason]

Imagine being given the sin(3x) problem solution as something to be integrated, and you'd have to mess with the integral of sin^3(x), where if you where a trickster you'd just work this backwards

[giadapaolini]

Thank you very much for this explanation finally i can resolve the exercise on the book!!!

[Soup-man]

Thank you kind sir. I have a summer AP assignment to do after I forgot everything from precalculus. My brain almost exploded.

[adminguy]

While the whole video was 5'28'' long, I was impressed that Sir spent >50 seconds in explaining the addition of 2sinx - 2sin^3(x) + sin x - 2sin^3(x)...

[puremaths]

I don't have words to appreciate ur effort

[azzamlabib]

wow brilliant and detail explanation, what if you make video about olympiad problem solutions ? i would appreciate it so much!

[lizetholguin]

Omg! I kept trying to find out where the -2sin^3x was coming from. Thank you so much!

[reubenmanzo]

I've been trying to find a formula for sin(x/3). Could you help with that?

I got as far as 4sin^3(x/3)-3sin(x/3)+sin(x)=0, which we must solve for sin(x/3). Substituting sin(x/3) as our x variable and replacing sin(x) with a constant k, I entered this equation into a graphing calculator, which looks like y=4x^3-3x+k. Restricting the values of k to the range of sin(x) gives 3 roots to the cubic for all values of k. However, trying to use the cubic formula places sin^2x-1 under the square root.

[sully]

Thank you, this video has been a lifesaver.

[tokenup]

Do you have any videos that explain how to get the generalized form for power series? I am doing D.E.'s with power series and I am having trouble finding these. An ex is reccurrence relation Cn+1= -(2Cn-1/(n+1)
n=1 C2=-(2/2)(Co)
n=2 C3=0
n=3 C4= (2^2/2×4)(Co)
n=4 C5=0
n=5 C6= -(2^3/2×4×6)(Co)
n=6 C7=0
n=7 C8= (2^4/2×4×6×8)(Co)

not wanting you to solve it just guide me to some good examples of this and more difficult ones. I know it has an alternator (-1)^n and a 2n in the numerator.

[ChadEyye]

❤❤❤❤❤❤❤ thank you you so much I appreciate your effort

[WResearcher]

How do I know what quadrant 3x lies in? and what if there are already values?

[АйгеримАйгерим-см]

Thank u so much HUGE love and respect from Kazakhstan 🇰🇿 ❤❤❤❤. Sir u saved my life ❤ 💗

[shinable]

Thank you, can you also solve this: cos(7x) + cos(x) = 0

[tarkbugra]

Question wants inspiration thanks 4 the solution

[cdmaraveml]

Hi, can someone answer this question.
Derive the formula for sin 4x in terms of sinx and cosx?