sin(theta) is opposite/hypotenuse regarding right triangles. Then what would \sin(2theta)

Ann Tice 2021-11-20 Answered
sin(theta) is opposite/hypotenuse regarding right triangles. Then what would \(\displaystyle{\sin{{\left({2}\theta\right)}}}\) be?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Archie Griffin
Answered 2021-11-21 Author has 558 answers
The number \(\displaystyle{\sin{{2}}}\theta\) is the sin of twice the angle \theta. It is almost never equal to \(\displaystyle{2}{\sin{\theta}}\).
\(\displaystyle{\sin{{2}}}\theta={2}{\sin{\theta}}\times{\cos{\theta}}{\left({1}\right)}\) If you know that \(\displaystyle{\sin{\theta}}={x}{3}\), all you need to do to find \(\displaystyle{\sin{{2}}}\theta\) is to find \(\displaystyle{\cos{\theta}}\).
Have a similar question?
Ask An Expert
0
 
Abel Maynard
Answered 2021-11-22 Author has 586 answers

\(\displaystyle{\sin{{2}}}\theta\ne{2}{\sin{\theta}}\), but \(\displaystyle{4}{\sin{{2}}}\theta={2}{\sin{\theta}}{\cos{\theta}}\)
As we know, \(\cos2\theta\ne2\cos\theta, \cos2\theta=\sin2\theta−\cos2\theta=2\cos2\theta−1=1−2\sin2\theta\)

0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...