Question

if sin (theta) = x/3
then sin (2 theta) = 2x/3
is this true?

Answer 1

nope

Answer 2

not always

Answer 3

\[\sin \theta = \frac{ x }{ 3 }\]
\[\sin 2\theta = \frac{ 2x }{ 3 }\]
if no, then what is \[\sin 2\theta \]

Answer 4

\[\sin 2\theta=2 \sin \theta \cos \theta\]

Answer 5

\[\sin ^2 \theta +\cos ^2 \theta=1 \\cos^2 \theta=1-\sin ^2 \theta\\cos \theta =\pm \sqrt{1-\sin^2 \theta}\]

Answer 6

the original question was
\[\int\limits_{}^{} \frac{ 8 dx }{ (4x ^{2} +1)^{2} } \]

Answer 7

use substitution x=1/2 tan u
dx=1/2 (1+tan ^2 u+1) du