Cos(75°) = (√6 − √2)/4
Cosine — the x-coordinate of the corresponding unit-circle point, or adjacent/hypotenuse in a right triangle.
How to derive cos(75°)
Sum formula: cos(45° + 30°) = cos45°cos30° − sin45°sin30° = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4.
Unit-circle context
The angle 75° corresponds to 5π/12 radians and sits Quadrant I on the unit circle.
Other trig values at 75°
Related cos values
Frequently asked
- What is the exact value of cos(75°)?
- The exact value is (√6 − √2)/4. Its decimal approximation is 0.25882.
- How do you derive cos(75°)?
- Sum formula: cos(45° + 30°) = cos45°cos30° − sin45°sin30° = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4.
- What is 75° in radians?
- 75° equals 5π/12 radians (multiply degrees by π/180).
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