Sin(45°) = √2/2
Sine — the y-coordinate of the corresponding unit-circle point, or opposite/hypotenuse in a right triangle.
How to derive sin(45°)
A 45-45-90 right triangle with legs 1 has hypotenuse √2 by Pythagoras. So sin(45°) = opposite/hypotenuse = 1/√2 = √2/2.
Unit-circle context
The angle 45° corresponds to π/4 radians and sits Quadrant I on the unit circle.
Other trig values at 45°
Related sin values
Frequently asked
- What is the exact value of sin(45°)?
- The exact value is √2/2. Its decimal approximation is 0.70711.
- How do you derive sin(45°)?
- A 45-45-90 right triangle with legs 1 has hypotenuse √2 by Pythagoras. So sin(45°) = opposite/hypotenuse = 1/√2 = √2/2.
- What is 45° in radians?
- 45° equals π/4 radians (multiply degrees by π/180).
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