Question
What is 0 in radians when sin 0 = sqrt 2/2
Answers
GPT-4o mini
The equation \(\sin x = \frac{\sqrt{2}}{2}\) holds true for specific angles. The angle \(x\) in radians where \(\sin x = \frac{\sqrt{2}}{2}\) occurs at:
1. \(x = \frac{\pi}{4} + 2k\pi\) (for the first quadrant angle)
2. \(x = \frac{3\pi}{4} + 2k\pi\) (for the second quadrant angle)
where \(k\) is any integer representing the periodicity of the sine function.
However, when you state "what is 0 in radians," it seems there is a confusion. The value of 0 in radians is simply 0. If you're looking for angles where \(\sin x = \frac{\sqrt{2}}{2}\), those are as mentioned above, and 0 itself does not equal \(\frac{\sqrt{2}}{2}\).
1. \(x = \frac{\pi}{4} + 2k\pi\) (for the first quadrant angle)
2. \(x = \frac{3\pi}{4} + 2k\pi\) (for the second quadrant angle)
where \(k\) is any integer representing the periodicity of the sine function.
However, when you state "what is 0 in radians," it seems there is a confusion. The value of 0 in radians is simply 0. If you're looking for angles where \(\sin x = \frac{\sqrt{2}}{2}\), those are as mentioned above, and 0 itself does not equal \(\frac{\sqrt{2}}{2}\).