What are the possible values of sin x, and which one is not possible?

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The sine function, denoted as sin x, is a fundamental concept in trigonometry that represents the ratio of the length of the opposite side to the hypotenuse in a right triangle.

For any angle x, the value of sin x can range from -1 to 1. This means that no matter what angle you provide, the output will always be bounded within this range:

  • At 0° (or 0 rad), sin 0 = 0
  • At 90° (or π/2 rad), sin 90 = 1
  • At 180° (or π rad), sin 180 = 0
  • At 270° (or 3π/2 rad), sin 270 = -1
  • At 360° (or 2π rad), sin 360 = 0

Thus, the values of sin x can never be less than -1 or greater than 1. Any value outside of this interval, such as 2 or -3, is not a possible value of sin x.

In summary, the sine function is limited to the values between -1 and 1, inclusive. Therefore, any value outside this range cannot be achieved by sin x.

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