Question

How would I simplify this trig identity?

Answer 1

\[2\sin \frac{ \theta }{ 2 }\cos \frac{ \theta }{ 2 }\]

Answer 2

I'm getting \[\sqrt{1-cosA^2}\]

Answer 3

is that right..? @freckles

Answer 4

@TheSmartOne

Answer 5

@dan815 @jim_thompson5910

Answer 6

hmmm that is complicated, not simple

Answer 7

\[\sin(2\theta)=2\cos(\theta)\sin(\theta)\] should help

Answer 8

replace \(\theta\) by \(\frac{\theta}{2}\)

Answer 9

so sin(theta)=cos(sin)? that doesn't make sense

Answer 10

@freckles @misty1212

Answer 11

your ability to replace things is less then stellar ....

Answer 12

thanks

Answer 13

sin(2A) = 2 sin(A) cos(A)

when A = t/2 ....

sin(2 t/2) = 2 sin(t/2) cos(t/2)

Answer 14

the right side is what you have, the left side is the simplified equivalent.

Answer 15

Have you found the answer from what amistre said?

Answer 16

So, you know this trig identity:

\(\sf sin(2\theta)=2cos(\theta)sin(\theta)\)

And you can notice that the trig identity they gave you is:

\(\sf\large 2sin(\frac{\theta}{2})cos(\frac{\theta}{2})\)

Notice that from the trig identity we should have already memorized, that it has \(\sf \theta\) and in our problem it has \(\sf\large\frac{\theta}{2}\).

To make it easier for you to understand, lets change the variables:

\(\sf sin(2\theta)=2cos(\alpha )sin(\alpha)\)

and our problem:

\(\sf\large 2sin(\frac{\theta}{2})cos(\frac{\theta}{2})\)

So if you notice, that means if we relate the two identities to each other then:

\(\sf\large\alpha = \frac{\theta}{2}\)

So that means for your answer, just replace \(\sf \alpha \) with \(\sf\large\frac{\theta}{2}\) and just simplify it.

Answer 17

so sin(2(theta/2)

Answer 18

Exactly, and simplify that.

Answer 19

One last step, simplify this and you are done. :)
\(\sf\Large sin(2\times \frac{\theta}{2})\)

Answer 20

wouldn't that just be sin(theta)

Answer 21

Exactly!

Answer 22

aight good lucks man thank you!

Answer 23

:)

Answer 24

Great job @QualifiedHelper (: