Trigonometric Identities Question 132
Question: If $ \tan \theta =\frac{-4}{3}, $ then $ \sin \theta = $
[IIT 1979; Pb. CET 1995; Orissa JEE 2002]
Options:
A) - 4/5 but not 4/5
B) - 4/5 or 4/5
C) 4/5 but not - 4/5
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Since $ cose{c^{2}}\theta =1+{{\cot }^{2}}\theta =1+\frac{9}{16}=\frac{25}{16} $ $ ( \because \tan \theta =-\frac{4}{3} ) $ $ {{\sin }^{2}}\theta =\frac{1}{cose{c^{2}}\theta }=\frac{16}{25}\Rightarrow \sin \theta =\pm \frac{4}{5}, $ Both the values are acceptable, since $ \tan \theta =-\frac{4}{3} $ $ ,i.e.,\theta $ lies in $ 2^{nd} $ or $ 4^{th} $ quadrant.
BETA
