Trigonometric Equations Question 36
Question: One root of the equation $ \cos x-x+\frac{1}{2}=0 $ lies in the interval
[Kurukshetra CEE 1996]
Options:
A) $ [ 0,,\frac{\pi }{2} ] $
B) $ [ -\frac{\pi }{2},,0 ] $
C) $ [ \frac{\pi }{2},,\pi ] $
D) $ [ \pi ,\frac{3\pi }{2} ] $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ f(x)=\cos x-x+\frac{1}{2} $ , $ f(0)=\frac{3}{2}>0 $ $ f( \frac{\pi }{2} )=0-\frac{\pi }{2}+\frac{1}{2}=\frac{1-\pi }{2}<0 $ , $ ( \because \ \pi =\frac{22}{7}\text{ nearly} ) $ \ One root lies in the interval $ [ 0,,\frac{\pi }{2} ] $ .
BETA
