Sine in Degrees Calculator

Enter an angle in degrees to find its sine value, quadrant, reference angle, and exact value for common angles.

Enter Angle in Degrees

Result

sin(150°)
0.5
Sine Value0.5
Exact Value1/2
QuadrantII
Reference Angle30°
Sign in QuadrantPositive (+)
Radians2.617994 rad
cos(x)-0.866025
tan(x)-0.577350

Step-by-Step Solution

sin(150°) = sin(180° - 30°) = sin(30°) = 0.5

Sine Values by Quadrant

The unit circle is divided into four quadrants. The sign of sine depends on which quadrant the angle falls in. Sine is positive in Quadrants I and II (where y-coordinates are positive) and negative in Quadrants III and IV.

Quadrant Reference

Quadrant I (0° - 90°)

All trig functions are positive.

sin(+), cos(+), tan(+)

Quadrant II (90° - 180°)

Only sine is positive.

sin(+), cos(-), tan(-)

Quadrant III (180° - 270°)

Only tangent is positive.

sin(-), cos(-), tan(+)

Quadrant IV (270° - 360°)

Only cosine is positive.

sin(-), cos(+), tan(-)

Common Sine Values in Degrees

  • sin(0°) = 0
  • sin(30°) = 1/2 = 0.5
  • sin(45°) = √2/2 ≈ 0.7071
  • sin(60°) = √3/2 ≈ 0.8660
  • sin(90°) = 1
  • sin(120°) = √3/2 ≈ 0.8660
  • sin(135°) = √2/2 ≈ 0.7071
  • sin(150°) = 1/2 = 0.5
  • sin(180°) = 0
  • sin(270°) = -1
  • sin(360°) = 0

What is a Reference Angle?

The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis. It is always between 0° and 90°. The sine of any angle equals the sine of its reference angle (with appropriate sign based on quadrant).