Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.2 - Trigonometric Functions of Real Numbers - 5.2 Exercises - Page 416: 2


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. $\sin t=y \qquad \cos t=x\qquad \displaystyle \tan t=\frac{y}{x}$ $\displaystyle \csc t=\frac{1}{y}\qquad \displaystyle \sec t=\frac{1}{x}\qquad \displaystyle \cot t=\frac{x}{y}$ ------------------ 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 $\sin^{2}t+\cos^{2}t =1$
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