0

Graph $ \sin(x^3) $ I want to find the roots. I thought triple angle identity would lead to finding roots but I get a different graph. So this function is much different.
Here is the graph I am looking at enter image description here

Here is my mistake. I was wondering if someone could get me back on the right track? $\sin^3(x) =\frac34 \sin(x) - \frac14 \sin(3x)$

enter image description here

Trig
  • 565
  • 2
  • 12

1 Answers1

2

Don't overcomplicate matters with the triple angle identity. We know that $$ \sin \theta = 0 \text{ whenever } \theta = k \pi \text{ for some integer } k $$ Hence, if $\sin x^3 = 0$, then $$ x^3 = k \pi \text{ for some integer } k $$

PrincessEev
  • 50,606
  • Is there anyway I can find the period, $ \frac{2 \pi}{B} $ I am a little overwhelmed by it. It doesn't follow the usually pattern that I have studied. – Trig Apr 26 '24 at 12:14
  • Just take a look at the graph; it is $2\pi$-periodic (so $B=1$). Handling it more "properly" is a bit complicated (link). – PrincessEev Apr 26 '24 at 20:32