Unit Circle Calculator

The angle for a forward function (sin, cos, tan, …), read in the selected angle unit.
Result
0.7071067812
Trigonometry Function Calculator
Result unit
ratio
Angle
45.0000000000 deg
Angle
0.7853981634 rad
Angle
50.0000000000 grad
sin θ
0.7071067812
cos θ
0.7071067812
tan θ
1.0000000000
csc θ
1.4142135624
sec θ
1.4142135624
cot θ
1.0000000000
Quadrant
I
Reference angle
45.00000000 deg
Coterminal angle in [0°, 360°)
45.00000000 deg
Exact value
sin 45° = √2/2, cos 45° = √2/2
Expression
sin(45°) = 0.7071067812
Worked out from NIST Digital Library of Mathematical Functions, Chapter 4: Elementary Functions (trigonometric and inverse trigonometric) and 2 other sources.

How this is worked out

3 steps
  1. θ = 45 deg = 0.7853981634 rad (× π/180 for degrees)
  2. sin(45°) = 0.7071067812
  3. Coterminal angle in [0°, 360°) = 45°, quadrant I, reference angle 45°

Results are general information, not financial, tax, legal, medical or engineering advice.