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**1. Homework Statement**

The problem comes with a diagram but I'll use the wikipedia diagram because it's nice and pretty and I'll just rearrange the letters to suit it.

http://upload.wikimedia.org/wikipedia/commons/9/9d/Circle-trig6.svg

Just in case the image doesn't load in the page: http://upload.wikimedia.org/wikipedia/commons/9/9d/Circle-trig6.svg

Prove that AE = Tan([tex]\theta[/tex])

Similar triangles may help.

**2. Homework Equations**

Basic similar triangles equations of:

[tex]\frac{OF}{AC}[/tex] = [tex]\frac{OE}{AC}[/tex] = [tex]\frac{OA}{FE}[/tex]

**3. The Attempt at a Solution**

After working out the above relationship, I've tried to look specifically at the ACE triangle. I already have AC = sin([tex]\theta[/tex]) and EC = OE - cos([tex]\theta[/tex])

AE = [tex]\sqrt{(AC)^{2} + (EC)^{2}}[/tex]

I need to rearrange it somehow so I get: AE = [tex]\sqrt{\frac{sin^{2}(\theta)}{cos^{2}(\theta)}}[/tex] but I'm not sure how to go about this. I'm getting a bit lost/sidetracked so hopefully you can give me some help. There a part (b) in this question but I won't ask about that until after this and hopefully once I can solve this (b) will be easy.

Thanks in advance for your help.

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