Determine the exact value of 𝑥 the following expression given that 0 ≤ 𝑥 ≤ 90.
sinx=sqaureroot3/2
The given expression is sinx = sqrt(3)/2.
To determine the value of x, we need to find the angle whose sine is sqrt(3)/2.
In the unit circle, the sine of an angle is equal to the y-coordinate of its terminal point. Since the sine is positive (sqrt(3)/2 is positive), we know that the angle terminates in the first or second quadrant.
In the first quadrant (0 to 90 degrees), the only angle whose sine is sqrt(3)/2 is 60 degrees.
Therefore, the exact value of x is 60 degrees.