Trigonometry- Cos, Sin, Tan

Trigonometry- Cos, Sin, Tan

Trigonometry: Cos, Sin, Tan

Trigonometry involves the relations between the angles and sides of triangles. There are three main trigonometric ratios: Sine (Sin), Cosine (Cos), and Tangent (Tan).

Sine (Sin)

  • Sine is a trigonometric function defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle. This can be remembered with the mnemonic SOH (Sin = Opposite / Hypotenuse).
  • If θ is an angle of a right-angle triangle, then Sinθ = Opposite / Hypotenuse.

Cosine (Cos)

  • Cosine is a trigonometric function defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. This can be remembered with the mnemonic CAH (Cos = Adjacent / Hypotenuse).
  • If θ is an angle of a right-angle triangle, then Cosθ = Adjacent / Hypotenuse.

Tangent (Tan)

  • Tangent is a trigonometric function defined as the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle. This can be remembered with the mnemonic TOA (Tan = Opposite / Adjacent).
  • If θ is an angle of a right-angle triangle, then Tanθ = Opposite / Adjacent.

Finding Angles and Sides

  • To calculate an unknown side of a right-angle triangle, you can rearrange the trigonometric formulas.
  • To calculate an unknown angle, you can use the inverse functions of Sin, Cos, or Tan on your calculator (usually marked as Sin^-1, Cos^-1, Tan^-1).
  • Make sure your calculator is in degree mode when calculating angles.

Solving Trigonometric Problems

  • When solving trigonometric problems, it’s important to label the sides of the triangle correctly - Opposite, Adjacent, and Hypotenuse - based on the angle you are considering.
  • Use the appropriate trigonometric ratio (Sin, Cos, or Tan) based on what sides of the triangle are involved in the problem.

Remember, understanding and application of the trigonometric ratios (Sin, Cos, and Tan) are crucial aspects of the Angles and Geometry component of your syllabus. Keep practising a variety of problems to build up your skills.