First slide

Trigonometric Identities

Question

$If \sin θ < θ < \tan θ, then θ \in$

Moderate

A

$(0, \frac{3 π}{2})$
B

$(0, \frac{π}{2})$
C

$(- \frac{π}{2}, \frac{π}{2})$
D

$(0, π)$

Solution

consider a circle unit radius area of $Δ O B C <$ Area of sector OBC<Area of $Δ O B D$
$\begin{array}{l} = \frac{1}{2} \sin θ (1) < \frac{1}{2} θ < \frac{1}{2} (1) \tan θ \\ ∴ \sin θ < θ < \tan θ \end{array}$

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