Trigonometry

• What mathematical branch studies right angle triangles?

  Trigonometry
• What does trigonometry study in right angle triangles?

  Relationships between sides and angles
• How can trigonometry help with unknown side lengths?

  By using known angles and side lengths
• What is the name of the angle commonly used in trigonometry?

  Theta
• What is the hypotenuse in a right angle triangle?

  The longest side opposite the right angle
• How do we label the sides of a right angle triangle?

  Hypotenuse, opposite, adjacent
• What does the sine function represent?

  Ratio of opposite to hypotenuse
• What does the cosine function represent?

  Ratio of adjacent to hypotenuse
• What does the tangent function represent?

  Ratio of opposite to adjacent
• What mnemonic helps remember trigonometric functions?

  • Some Old Hags Can't Always Hack Their Old Age
  • Sine = Opposite / Hypotenuse
  • Cosine = Adjacent / Hypotenuse
  • Tangent = Opposite / Adjacent
• What is the first step in solving a trigonometric problem?

  Label the unknown sides
• In a triangle with angle 35° and hypotenuse 12 m, how do you find the opposite side?

  Use sine function: sin 35° = opposite / 12
• What is the value of sin 35° used in calculations?

  0.57
• What is the calculated length of the opposite side in the example?

  1. 88 m
• How do you isolate X in the equation sin 35° = X / 12?

  Multiply both sides by 12
• In a triangle with angle 48° and hypotenuse 15 m, how do you find the opposite side?

  Use tangent function: tan 48° = opposite / adjacent
• What is the value of tan 48° used in calculations?

  1. 11
• How do you isolate X in the equation tan 48° = 15 / X?

  Divide 15 by tan 48°
• What is the calculated length of the adjacent side in the example?

  1. 51 m
• How do you find an angle using side lengths in trigonometry?

  Use inverse trigonometric functions
• In a triangle with sides 105 m and 33 m, how do you find angle Theta?

  Use sine function: sin Theta = 33 / 105
• What is the calculated value of sin Theta in the example?

  0.314
• How do you find Theta after calculating sin Theta?

  Use the inverse sine function
• What is the calculated angle Theta in the example?

  18.3°
• In a triangle with sides 17 m and 12 m, how do you find angle Theta?

  Use cosine function: cos Theta = 12 / 17
• What is the calculated value of cos Theta in the example?

  0.71
• How do you find Theta after calculating cos Theta?

  Use the inverse cosine function
• What is the calculated angle Theta in the example?

  45.1°
• What are the key steps in solving trigonometric problems?

  1. Label the sides (hypotenuse, opposite, adjacent)
  2. Identify the appropriate trigonometric function
  3. Substitute known values into the function
  4. Solve for the unknown variable
  5. Use inverse functions if necessary to find angles
• The cosine function is the ratio of the adjacent side to the hypotenuse.
• The sine function is the ratio of the side opposite an angle to the hypotenuse.
• The tangent function is the ratio of the opposite side to the adjacent side.
• The cotangent function is the reciprocal of the tangent function.
• The tangent function is the ratio of the side opposite an angle to the adjacent side.
• The sine function is the ratio of the opposite side to the hypotenuse.
• The cosecant function is the reciprocal of the sin function.
• The secant function is the reciprocal of the cosine function.
• The cosecant function is the reciprocal of the sinusoidal function.