Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises - Page 54: 64

Answer

$\csc$ 60$^{\circ}$ = $\frac{2\sqrt 3}{3}$

Work Step by Step

$\csc$ 60$^{\circ}$ We must find side $x$ of the 30$^{\circ}$ - 60$^{\circ}$ Right Triangle. Pythagorean Theorem: $c$$^{2}$ = $a$$^{2}$ + $b$$^{2}$ 2$^{2}$ = 1$^{2}$ + $x$$^{2}$ 4 = 1 + $x$$^{2}$ x$^{2}$ = 3 x = $\sqrt 3$ Now consider the triangle from the perspective of the 60$^{\circ}$ angle. Hypotenuse = 2 Opposite = $\sqrt 3$ Adjacent = 1 $\csc$ 60$^{\circ}$ = $\frac{Hypotenuse}{Opposite}$ = $\frac{2}{\sqrt 3}$ = $\frac{2\sqrt 3}{3}$ Therefore: $\csc$ 60$^{\circ}$ = $\frac{2\sqrt 3}{3}$
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