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COMEDK2024Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Evaluate : ⁻¹ [ (-680^ ) ]+ ⁻¹ [ (-600^ ) ]- ⁻¹ ( 270^ )

Options

  1. A14 9
  2. B- 4 9
  3. C- 5 9

Correct answer

C. - 5 9

Step-by-step solution

The expression is E = ⁻¹( (-680^ )) + ⁻¹( (-600^ )) - ⁻¹( 270^ ) . First, simplify the angles: (-680^ ) = (680^ ) = (720^ - 40^ ) = (-40^ ) = (40^ ) . Since 40^ [0, 180^ ] , ⁻¹( 40^ ) = 40^ . Next, (-600^ ) = - (600^ ) = - (720^ - 120^ ) = -(- 120^ ) = 120^ = (180^ - 60^ ) = 60^ . Since 60^ [- /2, /2] , ⁻¹( 60^ ) = 60^ . Finally, 270^ = -1 . ⁻¹(-1) = 180^ . Substituting these values into the expression: E = 40^ + 60^ - 180^ = 100^ - 180^ = -80^ . Convert -80^ to radians: -80 180 = - 8 18 = - 4 9 . Answer: - 4 9

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