Trigonometry

[igs]

The Radius of the circle in the following figure is 1 unit. Express the lengths OA, AB, and DC in terms of α (Alpha)

So for OA I started:

• cosα= OA/1
• cosα=OA
• α=cos^-1(OA)

for AB

• sinα= AB/1
• sinα= AB
• α=sin^-1(AB)

I'm not sure if i did them right and for the last one DC, I stated that DC=AB but after that i have no idea on what to do.
Any help would be appreciated
Thank You

 

[Ishuda]

What is DC/OC = DC/1 = DC in terms of \(\displaystyle \alpha\)?

 

[HallsofIvy]

The Radius of the circle in the following figure is 1 unit. Express the lengths OA, AB, and DC in terms of α (Alpha)
View attachment 4633
So for OA I started:

• cosα= OA/1
• cosα=OA
• α=cos^-1(OA)

for AB

• sinα= AB/1
• sinα= AB
• α=sin^-1(AB)

If the problem says "Express the lengths of OA, AB, and DC in terms of \(\displaystyle \alpha\)", there is no reason to solve for \(\displaystyle \alpha\).

I'm not sure if i did them right and for the last one DC, I stated that DC=AB but after that i have no idea on what to do.
Any help would be appreciated
Thank You

I would think it would be obvious that DC is NOT equal to AB!
DC is tangent to the circle. Perhaps you should think in terms of the tangent function.