Answer
Fill the blanks with
$1,\qquad $and$\qquad 1$
Work Step by Step
See p. 409, Definition of the Trigonometric Functions
Let $P(x, y)$ be the terminal point on the unit circle determined by the real number $t$.
Then for nonzero values of the denominator the trigonometric functions are defined as follows.
$\sin t=y \qquad \cos t=x\qquad \displaystyle \tan t=\frac{y}{x}$
$\displaystyle \csc t=\frac{1}{y}\qquad \displaystyle \sec t=\frac{1}{x}\qquad \displaystyle \cot t=\frac{x}{y}$
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The unit circle (has radius 1), centered at (0,0)
has an equation: $\quad x^{2}+y^{2}=1.$
Using the above definitions $(x=\cos t, y=\sin t$) substituting for x and y,
we get
$\sin^{2}t+\cos^{2}t =1$