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Question

Question: If \(\theta\) is...

If θ\theta is

A

π3\frac { \pi } { 3 }

B

π2\frac { \pi } { 2 }

C

2π3\frac { 2 \pi } { 3 }

D

−2π3- \frac { 2 \pi } { 3 }

Answer

π3\frac { \pi } { 3 }

Explanation

Solution

θ=sin⁡−1[sin⁡(−600∘)]\theta = \sin ^ { - 1 } \left[ \sin \left( - 600 ^ { \circ } \right) \right] = sin⁡−1[−sin⁡(360+240)]\sin ^ { - 1 } [ - \sin ( 360 + 240 ) ]

⇒ =sin⁡−1[−sin⁡(180∘+60∘)]= \sin ^ { - 1 } \left[ - \sin \left( 180 ^ { \circ } + 60 ^ { \circ } \right) \right]

⇒ =sin⁡−1[sin⁡(π3)]=π3= \sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 3 } \right) \right] = \frac { \pi } { 3 }