Trigonometry Basics: Sine Values
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Questions and Answers

If sin A = 1/3 in a right triangle ABC, what is the ratio of the lengths of sides BC and AC?

  • 1:2
  • 2:3
  • 3:4
  • 1:3 (correct)

    • If tan A = 3/4, what is the value of cos A?

  • 3/4
  • 4/5 (correct)
  • 3/5
  • 5/6

    • If cos A = 2/3, what is the value of sin A?

  • 1/2
  • 1/√5 (correct)
  • √5/3
  • 1/3

    • If AB = 2√2 k, what is the value of cot A?

    <p>1/2</p> Signup and view all the answers

    If AC = 5k, what is the value of sec A?

    <p>5/3</p> Signup and view all the answers

    If sin A = 1/2, what is the value of cos A?

    <p>√3/2</p> Signup and view all the answers

    If tan A = 1/2, what is the value of cot A?

    <p>2/3</p> Signup and view all the answers

    If cos A = 3/5, what is the value of sin A?

    <p>2/5</p> Signup and view all the answers

    If AB = 3k, what is the value of tan A?

    <p>2/3</p> Signup and view all the answers

    If AC = 3√2 k, what is the value of csc A?

    <p>3/√2</p> Signup and view all the answers

    Study Notes

    Trigonometric Ratios

    • The table shows the values of trigonometric ratios for angles 0° to 90°:
      • sin A: 0 to 1
      • cos A: 1 to 0
      • tan A: 0 to not defined
      • cosec A: not defined to 1
      • sec A: 1 to not defined
      • cot A: not defined to 0

    Using Trigonometric Ratios

    • Example: In a right-angled triangle ABC, with AB = 5 cm and ∠ACB = 30°, find the lengths of BC and AC.
    • To find the length of BC, use the trigonometric ratio involving BC and the given side AB.

    Trigonometric Identities

    • A trigonometric identity is an equation involving trigonometric ratios of an angle that is true for all values of the angle(s) involved.
    • Example: In a right-angled triangle ABC, with AB^2 + BC^2 = AC^2, we can derive the identity:
      • cos^2 A + sin^2 A = 1
      • 1 + tan^2 A = sec^2 A

    Finding Trigonometric Ratios

    • If we know one trigonometric ratio, we can find the others.
    • Example: If sin A = 1/3, then we can find the lengths of the sides of the triangle and hence the other trigonometric ratios.

    Important Points

    • The value of sin A or cos A is always less than 1 (or equal to 1) in a right triangle.
    • The hypotenuse is the longest side in a right triangle.

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    Description

    This quiz covers the basics of trigonometry, including sine values for different angles. Test your understanding of trigonometric concepts and formulas.

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