Trigonometry Basics Quiz
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Questions and Answers

What is the origin of the word 'trigonometry'?

  • Greek words meaning triangle and measurement
  • French words meaning angle and measurement
  • Latin words meaning triangle and measurements (correct)
  • Arabic words meaning angle and length

    • Clockwise rotation is represented as a positive direction.

    False

    What is the degree measurement of a full circle?

    360 degrees

    1 degree (1°) is equivalent to __________ minutes.

    <p>60</p> Signup and view all the answers

    Match the angle name with its representation:

    <p>Theta = θ Alpha = α Beta = β Phi = φ</p> Signup and view all the answers

    Which of the following correctly defines a ray?

    <p>A figure formed by one endpoint and extends infinitely in one direction</p> Signup and view all the answers

    What is the equivalent of π/2 radians in degrees?

    <p>90 degrees</p> Signup and view all the answers

    An angle is in standard position when its initial side is on the positive x-axis.

    <p>True</p> Signup and view all the answers

    What is the coterminal angle of -330° in the counter-clockwise direction?

    <p>30°</p> Signup and view all the answers

    The reference angle for 570° is 30°.

    <p>True</p> Signup and view all the answers

    What is the reference angle for 115°?

    <p>65°</p> Signup and view all the answers

    In Quadrant III, the reference angle is calculated using the formula RA = θ - ______.

    <p>180°</p> Signup and view all the answers

    Match the angles with their corresponding reference angle formulas:

    <p>Quadrant I = RA = θ Quadrant II = RA = 180° - θ Quadrant III = RA = θ - 180° Quadrant IV = RA = 360° - θ</p> Signup and view all the answers

    What is the coterminal angle of 2π/3 rad in the clockwise direction if calculated once?

    <p>-4π/3</p> Signup and view all the answers

    What is the reference angle for -π/6 rad?

    <p>π/6 rad</p> Signup and view all the answers

    The formula for coterminal angles in the counter-clockwise direction is θ + (360°)(n).

    <p>True</p> Signup and view all the answers

    What is the radian equivalent of 240°?

    <p>$4π/3$ rad</p> Signup and view all the answers

    Two angles that add up to 180° are called complementary angles.

    <p>False</p> Signup and view all the answers

    What is the radian measure for 150°?

    <p>5π/6 rad</p> Signup and view all the answers

    The sum of two complementary angles is _____ degrees.

    <p>90</p> Signup and view all the answers

    Match the angles with their relationship type:

    <p>60° and 30° = Complementary 120° and 60° = Supplementary 45° and 45° = Complementary 105° and 75° = Supplementary</p> Signup and view all the answers

    Which of the following angles is coterminal with 360°?

    <p>-360°</p> Signup and view all the answers

    A coterminal angle can only be found by adding 360° or subtracting 180°.

    <p>False</p> Signup and view all the answers

    Convert 5π/6 radians to degrees.

    <p>150°</p> Signup and view all the answers

    Two angles whose sum is _____ are called supplementary.

    <p>180</p> Signup and view all the answers

    Study Notes

    Trigonometry

    • Originates from the Latin words "trigonon" (triangle) and "metria" (measurement)
    • Branch of mathematics dealing with relationships between triangles, angles, and their measurements.

    Angle

    • Formed by two rays sharing a common endpoint called the vertex.
    • Can be defined as the amount of space covered by the rotation of one ray.
    • The fixed ray is the initial side and the moving ray is the terminal side.

    Naming an Angle

    • Uses Greek alphabets (θ, φ, β, ω, α, γ), capital English letters with degree symbol (A°, B°, C°), or English letters with angle sign (∠A, ∠B, ∠C).

    Rotation of an Angle

    • Counter-clockwise rotation: opposite direction of clock movement, represented by a positive (+) sign.
    • Clockwise rotation: same direction as clock movement, represented by a negative (-) sign.

    Angle Measurement Units

    Degree (°)

    • Divides a whole circle into 360 parts.
    • One degree can be further divided into minutes (60') and seconds (60").
    • 1° = 60' = 3600"

    Radian (rad)

    • Standard unit of angle measurement.
    • Length of the arc or circumference of the unit circle.

    Angle Standard Position

    • Angle in standard position on the Cartesian plane has its initial side along the positive x-axis and its vertex at the origin.

    Conversion of Angle Units

    • Full circle: 360° = 2π rad

    • Half circle: 180° = π rad

    • Degrees to radians: Multiply degrees by π rad / 180 degrees.

    • Radians to degrees: Multiply radians by 180 degrees / π rad.

    Relationship Angles

    Complementary Angles

    • Two angles whose sum is 90° or π⁄2 rad.
    • Examples: 50° and 40°; 30° and 60°; π⁄2 rad and π⁄2 rad.

    Supplementary Angles

    • Two angles whose sum is 180° or π rad.
    • Examples: 120° and 60°; 100° and 80°; π⁄2 rad and 3⁄2 π rad.

    Coterminal Angles

    • Two angles with the same initial and terminal sides, regardless of the number of rotations.
    • Counter-clockwise: θ + (360°) (n) or θ + (2π) (n)
    • Clockwise: θ - (360°) (n) or θ - (2π) (n), where n is an integer.

    Reference Angles

    • Smallest positive acute angle between the terminal side of a given angle and the nearest x-axis.
    • Quadrant I: RA = θ
    • Quadrant II: RA = 180°-θ
    • Quadrant III: RA = θ - 180°
    • Quadrant IV: RA = 360°-θ
    • Radian:
      • Quadrant I: RA = θ
      • Quadrant II: RA = π - θ
      • Quadrant III: RA = θ - π
      • Quadrant IV: RA = 2π - θ

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    Description

    Test your knowledge on the fundamentals of trigonometry, including angles, their formation, and measurement units. This quiz covers essential concepts like angle rotation and naming conventions. Perfect for anyone looking to strengthen their math skills!

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