Trigonometrical ratios for various angles

The trigonometric ratios for common angles (0°, 30°, 45°, 60°, 90°) are often memorized and used frequently in calculations.

For θ=0°:sin(0°)=0,cos(0°)=1,tan(0°)=0For θ=30°:sin(30°)=12,cos(30°)=32,tan(30°)=13For θ=45°:sin(45°)=cos(45°)=22,tan(45°)=1For θ=60°:sin(60°)=32,cos(60°)=12,tan(60°)=3For θ=90°:sin(90°)=1,cos(90°)=0(undefined),tan(90°)=(undefined)
 

1. Sine (sin):

  • Definition: sin(θ)=Opposite sideHypotenuse
  • Common Values:
    • sin(0)=0
    • sin(30)=12
    • sin(45)=22
    • sin(60)=32
  •  

2. Cosine (cos):

  • Definition: cos(θ)=Adjacent sideHypotenuse
  • Common Values:
    • cos(0)=1
    • cos(30)=32
    • cos(45)=22
    • cos(60)=12
    • cos(90)=0

3. Tangent (tan):

  • Definition: tan(θ)=Opposite sideAdjacent side
  • Common Values:
    • tan(0)=0
    • tan(30)=13
    • tan(45)=1
    • tan(60)=3
    • tan(90)=Undefined
  •  

4. Cosecant (csc), Secant (sec), Cotangent (cot):

  • Cosecant: csc(θ)=1sin(θ)
  • Secant: sec(θ)=1cos(θ)
  • Cotangent: cot(θ)=1tan(θ)

Important Points:

  • Trigonometric ratios are defined for all acute angles in a right-angled triangle.
  • In the unit circle, trigonometric ratios can be extended to any angle.
  • For complementary angles (angles that add up to 90 degrees), the sine and cosine ratios are complementary (i.e., sin(θ)=cos(90θ) and vice versa).