Simplify $x^2sinleft(fracx2right)cosleft(fracx2right)$
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In this problem I need to simplify the following expression:
$$x^2sinfracx2cosfracx2$$
However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)
trigonometry
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up vote
2
down vote
favorite
In this problem I need to simplify the following expression:
$$x^2sinfracx2cosfracx2$$
However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)
trigonometry
2
Use $sin 2x=2sin xcos x$.
â Lord Shark the Unknown
Aug 26 at 10:58
2
$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
â Jendrik Stelzner
Aug 26 at 10:59
@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
â Pablo
Aug 26 at 11:00
The given expression, a product of algebra and trig, is as simple as it can get.
â Narasimham
yesterday
this requires you to know $sin(a+b)$
â Nick
yesterday
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
In this problem I need to simplify the following expression:
$$x^2sinfracx2cosfracx2$$
However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)
trigonometry
In this problem I need to simplify the following expression:
$$x^2sinfracx2cosfracx2$$
However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)
trigonometry
edited yesterday
Nick
3,61973261
3,61973261
asked Aug 26 at 10:57
Pablo
33312
33312
2
Use $sin 2x=2sin xcos x$.
â Lord Shark the Unknown
Aug 26 at 10:58
2
$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
â Jendrik Stelzner
Aug 26 at 10:59
@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
â Pablo
Aug 26 at 11:00
The given expression, a product of algebra and trig, is as simple as it can get.
â Narasimham
yesterday
this requires you to know $sin(a+b)$
â Nick
yesterday
add a comment |Â
2
Use $sin 2x=2sin xcos x$.
â Lord Shark the Unknown
Aug 26 at 10:58
2
$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
â Jendrik Stelzner
Aug 26 at 10:59
@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
â Pablo
Aug 26 at 11:00
The given expression, a product of algebra and trig, is as simple as it can get.
â Narasimham
yesterday
this requires you to know $sin(a+b)$
â Nick
yesterday
2
2
Use $sin 2x=2sin xcos x$.
â Lord Shark the Unknown
Aug 26 at 10:58
Use $sin 2x=2sin xcos x$.
â Lord Shark the Unknown
Aug 26 at 10:58
2
2
$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
â Jendrik Stelzner
Aug 26 at 10:59
$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
â Jendrik Stelzner
Aug 26 at 10:59
@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
â Pablo
Aug 26 at 11:00
@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
â Pablo
Aug 26 at 11:00
The given expression, a product of algebra and trig, is as simple as it can get.
â Narasimham
yesterday
The given expression, a product of algebra and trig, is as simple as it can get.
â Narasimham
yesterday
this requires you to know $sin(a+b)$
â Nick
yesterday
this requires you to know $sin(a+b)$
â Nick
yesterday
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
6
down vote
accepted
Recall that
$$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$
therefore with $theta=frac x 2$ we have
$$x^2sinfracx2cosfracx2=frac12x^2sin x$$
add a comment |Â
up vote
1
down vote
$$ sin x = 2 sin (x/2) cos (x/2) $$
Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$
No more simplification is possible.
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
accepted
Recall that
$$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$
therefore with $theta=frac x 2$ we have
$$x^2sinfracx2cosfracx2=frac12x^2sin x$$
add a comment |Â
up vote
6
down vote
accepted
Recall that
$$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$
therefore with $theta=frac x 2$ we have
$$x^2sinfracx2cosfracx2=frac12x^2sin x$$
add a comment |Â
up vote
6
down vote
accepted
up vote
6
down vote
accepted
Recall that
$$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$
therefore with $theta=frac x 2$ we have
$$x^2sinfracx2cosfracx2=frac12x^2sin x$$
Recall that
$$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$
therefore with $theta=frac x 2$ we have
$$x^2sinfracx2cosfracx2=frac12x^2sin x$$
answered Aug 26 at 10:59
gimusi
70.1k73786
70.1k73786
add a comment |Â
add a comment |Â
up vote
1
down vote
$$ sin x = 2 sin (x/2) cos (x/2) $$
Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$
No more simplification is possible.
add a comment |Â
up vote
1
down vote
$$ sin x = 2 sin (x/2) cos (x/2) $$
Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$
No more simplification is possible.
add a comment |Â
up vote
1
down vote
up vote
1
down vote
$$ sin x = 2 sin (x/2) cos (x/2) $$
Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$
No more simplification is possible.
$$ sin x = 2 sin (x/2) cos (x/2) $$
Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$
No more simplification is possible.
answered Aug 26 at 11:07
Mohammad Riazi-Kermani
30.5k41852
30.5k41852
add a comment |Â
add a comment |Â
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2
Use $sin 2x=2sin xcos x$.
â Lord Shark the Unknown
Aug 26 at 10:58
2
$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
â Jendrik Stelzner
Aug 26 at 10:59
@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
â Pablo
Aug 26 at 11:00
The given expression, a product of algebra and trig, is as simple as it can get.
â Narasimham
yesterday
this requires you to know $sin(a+b)$
â Nick
yesterday