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 Post subject: Establish Identity
PostPosted: Fri, 27 Apr 2012 07:17:32 UTC 
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sin(pi/2+theta)=cos(theta)


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 Post subject: Re: Establish Identity
PostPosted: Fri, 27 Apr 2012 07:20:09 UTC 
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The Duke wrote:
sin(pi/2+theta)=cos(theta)


Use the sine sum identity.

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 Post subject: Re: Establish Identity
PostPosted: Fri, 27 Apr 2012 07:22:50 UTC 
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show me how


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 Post subject: Re: Establish Identity
PostPosted: Fri, 27 Apr 2012 07:26:17 UTC 
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The Duke wrote:
show me how


Nope. It's one step, if you cannot do that you need help from your teacher.

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 Post subject: Re: Establish Identity
PostPosted: Fri, 27 Apr 2012 12:54:18 UTC 
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Shadow wrote:
The Duke wrote:
sin(pi/2+theta)=cos(theta)


Use the sine sum identity.


... or look at the unit circle, or ...

But it seems the OP doesn't want to put in any work.

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\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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