If sin x = -1, x can be

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Solution

The correct options are
A

B

C

D

Since, sin x graph is periodic function with period 2 $π$ . So, we shall find the value of x when sin x = -1 in the interval of [0, 2 $π$ ) and then add or subtract 2 $π$ for other values of x.

sin x = -1

x = $270^{\circ}$

other values of x should be $270^{\circ}$ + $360^{\circ}$ = $630^{\circ}$

and

$270^{\circ}$ + $720^{\circ}$ = $990^{\circ}$

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If we take angles in clockwise direction

sin x = -1

x = $- 90^{\circ}$

for other angles subtract $- 360^{\circ}$ from previous angle

x = -90 - $360^{\circ}$ = $- 450^{\circ}$

x = -450 - $360^{\circ}$ = $- 810^{\circ}$

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So, all A, B, C, D options are correct.

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