First slide

Properties of ITF

Question

If $θ \in [4 π, 5 π],$ then $\cos^{- 1} (\cos θ)$ equals

Moderate

A

$- 4 π + θ$
B

$5 π - θ$
C

$4 π - θ$
D

$θ - 5 π$

Solution

We have,
$θ \in [4 π, 5 π] \Rightarrow - 4 π + θ \in [0, π]$
Also,
$\begin{array}{l} \cos (- 4 π + θ) = \cos (4 π - θ) = \cos θ \\ ∴ \cos^{- 1} (\cos θ) = \cos^{- 1} {\cos (- 4 π + θ) ξ = - 4 π + θ \end{array}$

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