First slide

Trigonometric equations

Question

The least positive root of the function $\sin x - π / 2 + 1 = 0$ lies in the interval

Moderate

A

$[0, π / 2]$
B

$[π / 2, π]$
C

$[π / 2, 3 π / 2]$
D

none of these

Solution

$\sin x = \frac{π}{2} - 1 = \frac{22}{14} - 1 = \frac{8}{14}$
$= \frac{4}{7}$ so the least positive root lies in $[0, π / 2]$

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