Sin(105°) = (√6 + √2)/4
Sine — the y-coordinate of the corresponding unit-circle point, or opposite/hypotenuse in a right triangle.
How to derive sin(105°)
105° lies in quadrant II where sine is positive. The reference angle is 180° − 105° = 75°, so sin(105°) = sin(75°) = (√6 + √2)/4. Equivalently, sin(60° + 45°) gives the same value.
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 sin(105°) shares its absolute value with sin(75°).
Other trig values at 105°
Related sin values
Frequently asked
- What is the exact value of sin(105°)?
- The exact value is (√6 + √2)/4. Its decimal approximation is 0.96593.
- How do you derive sin(105°)?
- 105° lies in quadrant II where sine is positive. The reference angle is 180° − 105° = 75°, so sin(105°) = sin(75°) = (√6 + √2)/4. Equivalently, sin(60° + 45°) gives the same value.
- What is 105° in radians?
- 105° equals 7π/12 radians (multiply degrees by π/180).
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