trigonometry - quarter four

• Triangle


  A three-sided polygon
• Parts of a right triangle

  • Adjacent side
  • Reference angle
  • Opposite side
  • Hypotenuse
• Reference angle


  The acute angle between the terminal side and the x-axis. It is always positive and indicated by the symbol theta "θ".
• Opposite side


  The side across the reference angle in a right triangle
• Adjacent side


  The non-hypotenuse side next to the reference angle in a right triangle
• Hypotenuse


  The longest side of a triangle, always opposite the 90° angle in a right triangle
• All right triangles with a given acute angle measure are similar by AA similarity theorem
• The lengths of corresponding sides are proportional as well for similar triangles
• Sine


  The ratio of the opposite side to the hypotenuse of a right triangle
• The six trigonometric ratios

  • Sine (sin)
  • Cosine (cos)
  • Tangent (tan)
  • Cosecant (csc)
  • Secant (sec)
  • Cotangent (cot)
• Solving right triangles given two parts

  1. Find the missing side using Pythagorean theorem

  2. Find trigonometric ratios using SOH, CAH, TOA
• Pythagorean theorem


  a^2 + b^2 = c^2, where c is the hypotenuse of the triangle
• The hypotenuse is the longest side of a right triangle, opposite the 90 degree angle
• Six basic trigonometric ratios

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


  Opposite side / Hypotenuse
• Cosine ratio


  Adjacent side / Hypotenuse
• Tangent ratio


  Opposite side / Adjacent side
• Cotangent ratio


  Adjacent side / Opposite side
• Secant ratio


  Hypotenuse / Adjacent side
• Cosecant ratio


  Hypotenuse / Opposite side
• Sine is the reciprocal of Cosecant


  • Cosine is the reciprocal of Secant
  • Tangent is the reciprocal of Cotangent
• SOHCAHTOA


  Mnemonic for remembering trigonometric ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent
• The tangent function is the ratio of the side opposite to an angle, divided by the adjacent side.
• The cosine function is the ratio of the adjacent side to the length of the hypotenuse.
• The tangent function is the ratio of the opposite side to the adjacent side.
• The sine function is the ratio of the side opposite to an angle, divided by the length of the hypotenuse.
• To use the Pythagorean theorem, square both legs and add them together to get the value of the hypotenuse squared.
• Trigonometric functions are used to find unknown sides or angles in right triangles.
• The cosecant function is the reciprocal of the sine function.
• The cotangent function is the reciprocal of the tangent function.
• In a right triangle, the longest side is called the hypotenuse (c). The other two sides are called legs (a and b).
• The secant function is the reciprocal of the cosine function.
• In a right triangle, the longest side (the one with the largest measurement) is called the hypotenuse.
• In a right triangle, the longest side (the one with the largest measurement) is called the hypotenuse.
• Angle of elevation is the angle from the horizontal to the line of sight of the observer to the object above
• Angle of depression is the angle from the horizontal to the line of sight of the observer to the object below
• Horizontal Line of Sight


  An imaginary line that connects the eye of an observer to the object being observed
• Angle of Elevation


  The angle from the horizontal to the line of sight of the observer to the object above
• Angle of Depression


  The angle from the horizontal to the line of sight of the observer to the object below
• Classify Me!


  1. Angle of Elevation

  2. Angle of Depression