MATH

• Trigonometry


  The branch of mathematics that deals with the relation between the sides and angles of a triangle
• Right triangle trigonometry


  Used to find the length of one side or the measure of an acute angle of a right triangle
• Right triangle


  • Hypotenuse is the side opposite the right angle and the longest side
  • Opposite side is the side opposite an angle
  • Adjacent side is the side which is also a side of the angle
• Six trigonometric ratios


  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent
• Sine


  Opposite side over hypotenuse
• Cosine


  Adjacent side over hypotenuse
• Tangent


  Opposite side over adjacent side
• Cosecant


  Hypotenuse over opposite side (reciprocal of sine)
• Secant


  Hypotenuse over adjacent side (reciprocal of cosine)
• Cotangent


  Adjacent side over opposite side (reciprocal of tangent)
• Finding six trigonometric ratios

  1. Identify opposite, adjacent, and hypotenuse sides

  2. Apply sine, cosine, and tangent formulas

  3. Calculate reciprocals for cosecant, secant, and cotangent
• Pythagorean theorem: c^2 = a^2 + b^2
• Right triangle


  • Triangle ABC with sides 4, 3, 5
• Right triangle


  • Triangle XYZ with sides 17, x, 15
• Solving for x


  1. 17 squared minus 15 squared

  2. Square root of 64 is 8

  3. Find value of x
• Trigonometric ratios


  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent
• Finding trigonometric ratios


  1. Opposite over hypotenuse

  2. Adjacent over hypotenuse

  3. Opposite over adjacent
• Reciprocal of trigonometric ratios
• Finding missing side using Pythagorean theorem


  1. c^2 = a^2 + b^2

  2. Find f
• Rationalizing denominator


  Multiply numerator and denominator by square root
• Finding trigonometric ratios given sine

  1. Use Pythagorean theorem to find other sides

  2. Calculate remaining ratios
• Finding trigonometric ratios given tangent

  1. Use Pythagorean theorem to find hypotenuse

  2. Calculate cosine and tangent of another angle
• Finding equation/formula to find missing part of triangle

  1. Use trigonometric ratios (cosine, sine, tangent)

  2. Solve for missing side or angle