Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapters 1-3 - Cumulative Test - Page 176: 9

Answer

$\sin^2{\theta} - 4\sin{\theta} - 21$

Work Step by Step

RECALL: $(a+b)(c+d)=ac + ad + bc + bd$ (more popularly known as the FOIL method). Use the formula above to multiply the binomials to obtain: $(\sin{\theta} + 3)(\sin{\theta} - 7) \\=\sin{\theta}(\sin{\theta}) + \sin{\theta} \cdot (-7) + 3\sin{\theta}+3(-7) \\=\sin^2{\theta}-7\sin{\theta}+3\sin{\theta} - 21 \\=\sin^2{\theta} - 4\sin{\theta} - 21$
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