Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises: 47

Answer

2($\tan$$^{2}$ 120$^{\circ}$) + 3($\sin$$^{2}$ 150$^{\circ}$) - ($\cos$$^{2}$ 180$^{\circ}$) = $\frac{23}{4}$

Work Step by Step

2($\tan$$^{2}$ 120$^{\circ}$) + 3($\sin$$^{2}$ 150$^{\circ}$) - ($\cos$$^{2}$ 180$^{\circ}$) $\tan$ 120$^{\circ}$ = $-\sqrt3$ $\sin$ 150$^{\circ}$ = $\frac{1}{2}$ $\cos$ 180$^{\circ}$ = -1 Therefore: = 2(-$\sqrt3$)$^{2}$ + 3($\frac{1}{2}$)$^{2}$ -(-1)$^{2}$ = 6 + $\frac{3}{4}$ - 1 = $\frac{24 + 3 -4}{4}$ = $\frac{23}{4}$ 2($\tan$$^{2}$ 120$^{\circ}$) + 3($\sin$$^{2}$ 150$^{\circ}$) - ($\cos$$^{2}$ 180$^{\circ}$) = $\frac{23}{4}$
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