Trigonometry

• Trigonometry


  A powerful way to work out different lengths in different triangles and work out the angles of a triangle
• Trigonometry was discovered by Greek mathematicians many years ago
• Sin


  The ratio of the opposite side to the hypotenuse of a right-angled triangle
• The hypotenuse is always the longest side in a right-angled triangle, opposite the 90 degree angle
• Tan


  The opposite side of the angle divided by the adjacent
• Trig ratios


  1. Sin = opposite/hypotenuse

  2. Cos = adjacent/hypotenuse

  3. Tan = opposite/adjacent
• Tan of b


  • Opposite (eg) / Adjacent (ef)
• Calculate Tan if

  • Opposite (4) / Adjacent (3)
• Tan of b (green triangle)

  • Opposite (12) / Adjacent (5)
• calculate the Tan if the...

  • Opposite (5) / Adjacent (12)
• You need to remember the trig ratios for when you are in a test
• sin

  Opposite / Hypotenuse
• cos

  Adjacent / Hypotenuse
• tan

  Opposite / Adjacent
• Solving for x using trigonometric ratios

  1. Identify the given information (angle, side lengths)

  2. Determine which trigonometric ratio to use (sin, cos, or tan)

  3. Set up the equation using the ratio

  4. Solve for x by isolating it on one side of the equation