Find sin è/2 for cos è = 1/4 and è lies in Quadrant I.
follow the method in my previous post
To find sin(π/2), let's first find the value of sin(è) using the given information.
Given that cos(è) = 1/4, we can use the Pythagorean identity to find sin(è):
sin²(è) + cos²(è) = 1
Since we know that cos(è) = 1/4, we can substitute the value into the equation:
sin²(è) + (1/4)² = 1
Rearranging the equation:
sin²(è) + 1/16 = 1
sin²(è) = 1 - 1/16
sin²(è) = 16/16 - 1/16
sin²(è) = 15/16
To solve for sin(è), take the square root of both sides of the equation:
sin(è) = ±√(15/16)
Since è lies in Quadrant I, the value of sin(è) is positive. Thus, we can take the positive square root:
sin(è) = √(15/16)
Simplifying the expression:
sin(è) = √(15)/√(16)
sin(è) = √(15)/4
Therefore, sin(π/2) or sin(90°) = √(15)/4.