While Baljeet is organizing his binder, he finds a conjecture that he wrote for problem 3-81: If one angle of a right triangle has the slope ratio $\frac { a } { b }$, then the complementary angle has a slope ratio of $\frac { b } { a }$.

1. How can Baljeet update the conjecture using the name of the trig ratio that corresponds to the slope ratio?

   Hint (a):

   Draw a sketch of a right triangle with the sides labeled correctly.

2. Write a new conjecture about the sine and cosine of complementary angles. You might try some examples on your calculator to help you develop your conjecture.

   Hint (b):

   Refer to your triangle sketch and remember that:

   $\sin(\theta)=\frac{\text{opp.}}{\text{hyp}.}$ and $\cos(\theta)=\frac{\text{adj.}}{\text{hyp.}}$