First slide

Extreme values and Periodicity of Trigonometric functions

Question

One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval

Easy

A

$(0, \frac{π}{2})$
B

$(\frac{- π}{2}, 0)$
C

$(\frac{π}{2}, π)$
D

$(π, \frac{3 π}{2})$

Solution

$L e t f (x) = \cos x - x + \frac{1}{2}$
$W e c a n s e e t h a t f (0) > 0, f (\frac{π}{2}) < 0$
$\Rightarrow f (x) = 0 h a s a t l e a s t o n e r o o t i n (0, \frac{π}{2})$

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