Which value equals sin(π/4)?

Which value equals sin(π/4)?

• A. sqrt(2)/2
• B. 1/2
• C. 0
• D. sqrt(3)/2

Answer: (A)

Sine corresponds to the y-coordinate on the unit circle. For an angle of π/4 (45 degrees) the point on the unit circle is (√2/2, √2/2), so the sine is the y-coordinate, giving sin(π/4) = √2/2. This also matches the 45-45-90 triangle intuition: with a unit hypotenuse, the equal legs are √2/2 each. Values like 1/2 or √3/2 correspond to other standard angles (π/6 or π/3), and 0 corresponds to angles like 0 or π, so sin(π/4) is the √2/2 result.

Sine corresponds to the y-coordinate on the unit circle. For an angle of π/4 (45 degrees) the point on the unit circle is (√2/2, √2/2), so the sine is the y-coordinate, giving sin(π/4) = √2/2. This also matches the 45-45-90 triangle intuition: with a unit hypotenuse, the equal legs are √2/2 each. Values like 1/2 or √3/2 correspond to other standard angles (π/6 or π/3), and 0 corresponds to angles like 0 or π, so sin(π/4) is the √2/2 result.