Which of the following values is NOT a solution for the equation 1 = sin( ? )?

To determine which value is not a solution for the equation (1 = \sin(\theta)), we need to identify when the sine function equals 1. The sine function reaches a value of 1 at specific angles in the unit circle. The principal angle where this occurs is at 90 degrees, or (\frac{\pi}{2}) radians.

Additionally, sine is a periodic function, meaning it repeats its values at regular intervals. The sine function has a period of 360 degrees, meaning that ( \sin(\theta) = 1 ) occurs at ( \theta = 90 + 360k ) for any integer ( k ). This means other equivalent angles, such as 450 degrees (which is (90 + 360)), are also solutions.

Now, let's consider each of the given angles:

• At -270 degrees, which is the same as 90 degrees (since -270 + 360 = 90), the sine value is 1.
• At 90 degrees, the sine value is 1, as this is a known solution.
• At 450 degrees, the sine value is also 1, confirming it as a solution as well.
• At 270 degrees