Trigonometry Fundamentals
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Questions and Answers

What is the measure of a straight angle?

  • 45°
  • 180° (correct)
  • 120°
  • 90°

    • What is the reciprocal of the sine function?

  • Tangent
  • Cosine
  • Cotangent
  • Cosecant (correct)

    • What is the formula for the tangent of the sum of two angles?

  • (tan(A) + tan(B)) / (1 - tan(A)tan(B)) (correct)
  • tan(A) + tan(B)
  • tan(A) - tan(B)
  • tan(A) * tan(B)

    • What is the Pythagorean identity in trigonometry?

    <p>sin^2(A) + cos^2(A) = 1</p> Signup and view all the answers

    What is the law of cosines used for?

    <p>Solving oblique triangles</p> Signup and view all the answers

    What is the amplitude of a trigonometric function?

    <p>The maximum value of the function</p> Signup and view all the answers

    What is the arctan function used for?

    <p>Solving equations involving trig functions</p> Signup and view all the answers

    What is the formula for the cosine of the sum of two angles?

    <p>cos(A)cos(B) - sin(A)sin(B)</p> Signup and view all the answers

    What is the difference between an acute angle and an obtuse angle?

    <p>An acute angle is less than 90°, while an obtuse angle is greater than 90°</p> Signup and view all the answers

    What is the formula for the law of sines?

    <p>a / sin(A) = b / sin(B) = c / sin(C)</p> Signup and view all the answers

    Study Notes

    Angles and Triangles

    • Angles:
      • Measured in degrees, radians, or revolutions
      • Can be acute (less than 90°), right (90°), obtuse (greater than 90°), or straight (180°)
    • Triangles:
      • Right triangles have one right angle (90°)
      • Oblique triangles have no right angles

    Trigonometric Ratios

    • Sine (sin):
      • Opposite side / Hypotenuse
      • sin(A) = opposite side / hypotenuse
    • Cosine (cos):
      • Adjacent side / Hypotenuse
      • cos(A) = adjacent side / hypotenuse
    • Tangent (tan):
      • Opposite side / Adjacent side
      • tan(A) = opposite side / adjacent side
    • Cotangent (cot):
      • Adjacent side / Opposite side
      • cot(A) = adjacent side / opposite side
    • Secant (sec):
      • Hypotenuse / Adjacent side
      • sec(A) = hypotenuse / adjacent side
    • Cosecant (csc):
      • Hypotenuse / Opposite side
      • csc(A) = hypotenuse / opposite side

    Trigonometric Identities

    • Pythagorean Identity:
      • sin^2(A) + cos^2(A) = 1
    • Sum and Difference Formulas:
      • sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
      • cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
      • tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

    Solving Triangles

    • Right Triangle Trigonometry:
      • Use trigonometric ratios to find missing sides or angles
    • Oblique Triangle Trigonometry:
      • Use law of sines and law of cosines to find missing sides or angles
    • Law of Sines:
      • a / sin(A) = b / sin(B) = c / sin(C)
    • Law of Cosines:
      • a^2 = b^2 + c^2 - 2bc * cos(A)

    Graphs and Inverse Trigonometric Functions

    • Graphs of Trigonometric Functions:
      • Sine, cosine, and tangent functions have periodic graphs
      • Amplitude, period, and phase shift can be modified
    • Inverse Trigonometric Functions:
      • arcsin, arccos, and arctan return angles in radians
      • Used to solve equations involving trigonometric functions

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    Description

    Test your understanding of trigonometry concepts, including angles, triangles, trigonometric ratios, identities, solving triangles, and graphs of trigonometric functions. This quiz covers various aspects of trigonometry, from basic definitions to advanced formulas and applications.

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