Find the Exact Value sin((pi/4)^2)

Problem

sin((π/4)2)

Solution

1. Square the argument inside the sine function by squaring both the numerator and the denominator.

(π/4)2=(π2)/16

2. Substitute the squared value back into the sine function.

sin((π2)/16)

3. Evaluate the expression. Since (π2)/16 is not a standard reference angle (it is approximately 0.61685 radians), the exact value is represented by the trigonometric expression itself.

Final Answer

sin((π/4)2)=sin((π2)/16)

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