Examine the diagram at right.  

1. Explain why $y=\sin\theta$ and $x=\cos\theta$.

   Hint (a):

   Use the diagram to write $\sin\theta=$ ?

2. According to this diagram, what is $\left(\sin\theta\right)^2+\left(\cos\theta\right)^2$? Explain how you know.

   Hint (b):

   Use the Pythagorean Theorem and your answer from part (a).

3. Does this relationship appear true for all angles? Use your calculator to find $\left(\sin23º\right)^2+\left(\cos23º\right)^2$ and $\left(\sin81º\right)^2+\left(\cos81º\right)^2$. Write down your findings.

   Answer (c):

   Yes.