Sin²(x)=0.25

Answer 1

There are two possible solutions to this equation:

1) x = 30 degrees or pi/6 radians
Taking the sine of 30 degrees, we get sin(30) = 0.5, so
sin²(30) = (0.5)² = 0.25

2) x = 150 degrees or 5pi/6 radians
Taking the sine of 150 degrees, we get sin(150) = -0.5 (since sine is negative in the second quadrant), so
sin²(150) = (-0.5)² = 0.25

Answer 2

actually, there are 4 solutions: 30°, 150°, 210°, 330°

Answer 3

You are correct. Since the sine function is periodic with a period of 360 degrees (or 2π radians), there are actually four solutions to the equation sin²(x) = 0.25 within one period:

1) x = 30 degrees or π/6 radians
Taking the sine of 30 degrees, we get sin(30) = 0.5, so
sin²(30) = (0.5)² = 0.25

2) x = 150 degrees or 5π/6 radians
Taking the sine of 150 degrees, we get sin(150) = -0.5 (since sine is negative in the second quadrant), so
sin²(150) = (-0.5)² = 0.25

3) x = 210 degrees or 7π/6 radians
Taking the sine of 210 degrees, we get sin(210) = -0.5 (since sine is negative in the third quadrant), so
sin²(210) = (-0.5)² = 0.25

4) x = 330 degrees or 11π/6 radians
Taking the sine of 330 degrees, we get sin(330) = 0.5 (since sine is positive in the fourth quadrant), so
sin²(330) = (0.5)² = 0.25

So, there are four solutions to the equation sin²(x) = 0.25 within one period.