Some Important rules:

• A line is a path joining a set of points in a plane.
• A portion of a line together with its dividing point, is known as a ray.
• A join or intersection of two rays having a common end point gives an angle. The common end point of an angle is called vertex of the angle. The rays that form the angle are called the sides of the angle.
• 90° is one measure of a Right Angle.
• Any angle measuring between 0° and 90° is called an acute angle.
• Any angle whose measure exceeds 90° but falls below 180° is called an abtuse angle.
• An angle between 180° and 360° is called reflex angle.
• When the rotating ray stops after making an angle of rotation ϑ, the place where the rotating ray stops is called the terminal side.
• If the ray has completed on full revolution about the vertex, then the angle turned is 360°

Sign of the trigonometric ratios in quadrants:-

1. All trigonometric ratios are positive in I quadrant.
2. Sine and cosec are positive in II quadrant.
3. Tan and cot are positive in III quadrant.
4. Cos and Sec are positive in IV quadrant.
5. Sexagesimal (English) system
6. Centesimal (French) system
7. The radian or circular measure.

Comeertion of Trigonometric Ratio to quadrants:-

Angles of the form ( nπ/2 + or - θ)

1. If n is even Sin Remains as sin : 
   Cos -- cos 
   Tan -- Tan 
   Cosec -- cosec 
   Sec -- sec 
   Cot -- cot


2. If n is odd Sin changes as cos : 
   Cos -- as Sin 
   Tan -- as Cot 
   Cot -- as Tan 
   Cosec -- as Sec 
   Sec -- as Cosec 

The values of trigonometric ratios of some standard angles:-

Some standard formulae:

• Sin θ = 1/cosec θ => sinθ.cosecθ = 1
• Cosθ = 1/secθ => cosθ.secθ = 1
• tanθ = 1/ cot => tanθ.cotθ = 1
• sin2θ+cos2θ = 1 => 1-cos2θ = sin2 and 1 - sin2θ = cos2θ
• sec2θ - tan2θ = 1 => 1+tan2θ = sec2θ and sec2θ - 1 = tan2θ
• cosec2θ - cot2θ = 1 => 1 + cot2θ = cosec2θ and cosec2θ - 1 = tan2θ
• sin2θ = 2sin θ cos θ
• cos2θ = 2sinθcosθ
• tan2θ = 2tanθ/1-tan2θ
• Sin (A+B) = SinA CosB + CosA SinB
• Sin (A-B) = SinA CosB - CosA SinB
• Cos (A+B) = CosA CosB - SinA SinB
• Cos (A-B) = CosA CosB + SinA SinB
• Tan (A+B) = (tan A + tan B)/(1-tan A tan B)
• Tan (A-B) = (tan A - tan B)/(1+tan A tan B)
• Sin 15° = Cos 75° = (√3 - 1)/2√2
• Cos 15° = Sin 75° = (√3 + 1)/2√2
• Tan 15° = Cot 75° = (√3 - 1)/(√23 + 1)

The values of trigonometric ratios of some standard angles:-

Complementary angles:

• If α,β are the complementary angles then
  1. sinα = cosβ
  2. cosα = sinβ
  3. tanα = cotβ
  4. cotα = tanβ
  5. sin2α + sin2β = 1
  6. cos2α + cos2β = 1
  7. tanα,tanβ = 1
  8. cotα,cotβ = 1
  1. If α,β are the supplementary angles then
      
     1. sinα = sinβ
     2. Sin (A-B) = SinA CosB - CosA SinB
     3. cosα + cosβ = 0
     4. tanα + tanβ = 0
     5. cotα + cotβ = 0
     6. sin2α + cos2β = 0
     7. cos2α + sin2β = 0
     
     
     
      
     8.  
  1. Sides of few right-angled triangles:
      
     1. 3, 4, 5
     
     
     2. 8, 15, 17
     
     
     3. 9, 40, 41