Trigonometric value

Sin(75°) = (√6 + √2)/4

Sine — the y-coordinate of the corresponding unit-circle point, or opposite/hypotenuse in a right triangle.

How to derive sin(75°)

sin(75°)=6+24sin(75°) = \dfrac{\sqrt{6}+\sqrt{2}}{4}

Sum formula: sin(45° + 30°) = sin45°cos30° + cos45°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 sin values

Frequently asked

What is the exact value of sin(75°)?
The exact value is (√6 + √2)/4. Its decimal approximation is 0.96593.
How do you derive sin(75°)?
Sum formula: sin(45° + 30°) = sin45°cos30° + cos45°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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