Trigonometry

    Cards (29)

    • 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 significance of the angle Theta in a right angle triangle?
      It determines the ratios of the sides
    • What is the longest side of a right angle triangle called?
      Hypotenuse
    • How is the opposite side labeled in a right angle triangle?
      O
    • How is the adjacent side labeled in a right angle triangle?
      A
    • What are the three main trigonometric functions?
      Sine, cosine, tangent
    • What does the sine function represent?
      Opposite over hypotenuse
    • What does the cosine function represent?
      Adjacent over hypotenuse
    • What does the tangent function represent?
      Opposite over adjacent
    • How can you remember the trigonometric functions' ratios?
      • 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 an angle of 35° and hypotenuse of 12 m, how do you find the opposite side?
      Use sine function
    • What is the sine of 35° approximately equal to?
      0.57
    • How do you isolate X in the equation sin(35°)=\sin(35°) =x12 \frac{x}{12}?

      Multiply both sides by 12
    • In a triangle with an angle of 48° and a known side length of 15 m, which function do you use to find the opposite side?
      Tangent function
    • What is the tangent of 48° approximately equal to?
      1.11
    • How do you find X in the equation tan(48°)=\tan(48°) =15X \frac{15}{X}?

      Divide 15 by 1.11
    • How do you find an angle using known side lengths?
      Use inverse trigonometric functions
    • In a triangle with sides 105 m and 33 m, which function do you use to find the angle?
      Sine function
    • What is the sine ratio for the sides 33 m and 105 m?
      0.314
    • How do you find Theta from sin(Θ)=\sin(\Theta) =0.314 0.314?

      Use the inverse sine function
    • What is the angle Theta when sin(Θ)=\sin(\Theta) =0.314 0.314?

      18.3°
    • In a triangle with sides 17 m and 12 m, which function do you use to find the angle?
      Cosine function
    • What is the cosine ratio for the sides 12 m and 17 m?
      0.71
    • How do you find Theta from cos(Θ)=\cos(\Theta) =0.71 0.71?

      Use the inverse cosine function
    • What is the angle Theta when cos(Θ)=\cos(\Theta) =0.71 0.71?

      45.1°
    • What are the key steps in solving trigonometric problems?
      1. Label the sides of the triangle
      2. Identify the appropriate trigonometric function
      3. Substitute known values
      4. Solve for the unknown
      5. Use inverse functions if needed