Cos(45°) = √2/2
Cosine — the x-coordinate of the corresponding unit-circle point, or adjacent/hypotenuse in a right triangle.
How to derive cos(45°)
A 45-45-90 right triangle is symmetric — both legs are 1 and hypotenuse √2. Sin and cos of 45° are equal: cos(45°) = 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 cos values
Frequently asked
- What is the exact value of cos(45°)?
- The exact value is √2/2. Its decimal approximation is 0.70711.
- How do you derive cos(45°)?
- A 45-45-90 right triangle is symmetric — both legs are 1 and hypotenuse √2. Sin and cos of 45° are equal: cos(45°) = 1/√2 = √2/2.
- What is 45° in radians?
- 45° equals π/4 radians (multiply degrees by π/180).
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