Cos(105°) = (√2 − √6)/4
Cosine — the x-coordinate of the corresponding unit-circle point, or adjacent/hypotenuse in a right triangle.
How to derive cos(105°)
105° is in quadrant II where cosine is negative. Reference angle = 180° − 105° = 75°, so cos(105°) = −cos(75°) = −(√6 − √2)/4 = (√2 − √6)/4.
Unit-circle context
The angle 105° corresponds to 7π/12 radians and sits Quadrant II on the unit circle.
Its reference angle is 75°, which is why cos(105°) shares its absolute value with cos(75°).
Other trig values at 105°
Related cos values
Frequently asked
- What is the exact value of cos(105°)?
- The exact value is (√2 − √6)/4. Its decimal approximation is -0.25882.
- How do you derive cos(105°)?
- 105° is in quadrant II where cosine is negative. Reference angle = 180° − 105° = 75°, so cos(105°) = −cos(75°) = −(√6 − √2)/4 = (√2 − √6)/4.
- What is 105° in radians?
- 105° equals 7π/12 radians (multiply degrees by π/180).
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