Had a test today.. need to know if I got this right.

[for]

There's a right triangle with hypotenuse 5.
I forget what the term was but it's between 0 and \(\displaystyle \frac{\pi}{2}\)

Anyway, solve for \(\displaystyle sin(2\theta)\)

I know that \(\displaystyle sin(2\theta) = 2sin\theta cos\theta\)

Is this just a simple 3 4 5 triangle? In which chase is the answer 24/25?

 

[BigGlenntheHeavy]

\(\displaystyle sin(2\theta) \ = \ sin(\theta+\theta) \ = \ sin(\theta)cos(\theta)+cos(\theta)sin(\theta), \ by \ sum \ formula,\)

\(\displaystyle = \ sin(\theta)cos(\theta)+sin(\theta)cos(\theta),multiplication \ is \ communative \ = \ voila! \ (a \ French \ word\)

\(\displaystyle pronounced \ walla \ as \ in \ Walla \ Walla, \ Wa., \ thank \ you \ galactus) \ 2sin(\theta)cos(\theta), \ property \ of\)

\(\displaystyle addition.\)