What value of ? satisfies the equation 1 = sin( ? )?

To determine the value that satisfies the equation ( 1 = \sin(? ) ), it's essential to understand the properties of the sine function in trigonometry. The sine function measures the ratio of the length of the opposite side to the hypotenuse in a right-angled triangle and has a range of values from -1 to 1.

The equation states that the sine of ( ? ) equals 1. This condition is met at specific angles along the unit circle. The sine function achieves a value of 1 at ( 90^\circ ) because this is the angle where the corresponding point on the unit circle reaches its maximum height.

Thus, ( ? = 90^\circ ) is the angle for which the sine is equal to 1. The other angles listed (360, 270, and 180) do not satisfy this condition because:

• At ( 360^\circ ), the sine function returns to 0, completing a full rotation.
• At ( 270^\circ ), the sine equals -1, which is below the target value of 1.
• At ( 180^\circ ), the sine also equals 0.

Therefore, the only angle from the provided choices that