Value of sin 45°: Exact Form 1/√2 & Decimal

How to derive it

In a right isosceles triangle with legs 1, the hypotenuse is √2 and both other angles are 45°.
sin = opposite ÷ hypotenuse, so sin 45° = 1/√2.

Angle	sin	cos	tan
15°	(√6 − √2)/4	(√6 + √2)/4	2 − √3
18°	(√5 − 1)/4	√(10 + 2√5)/4	√(25 − 10√5)/5
22.5°	√(2 − √2)/2	√(2 + √2)/2	√2 − 1
30°	1/2	√3/2	1/√3
36°	√(10 − 2√5)/4	(√5 + 1)/4	√(5 − 2√5)
45°	1/√2	1/√2	1
54°	(√5 + 1)/4	√(10 − 2√5)/4	√(25 + 10√5)/5
60°	√3/2	1/2	√3
67.5°	√(2 + √2)/2	√(2 − √2)/2	√2 + 1
72°	√(10 + 2√5)/4	(√5 − 1)/4	√(5 + 2√5)
75°	(√6 + √2)/4	(√6 − √2)/4	2 + √3

For whole-degree values from 0° to 90°, see the trigonometry table.

What is the value of sin 45°?

1/√2, which is about 0.7071.

What is sin 45° in radians?

45° is π/4 radians, so sin(π/4) = 1/√2.

Is sin 45° equal to cos 45°?

Yes. sin θ = cos(90° − θ), so sin 45° = cos 45°.