Trigonometric Angles: Elevation and Depression
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Questions and Answers

What is the range of angles of elevation?

  • 0° to 180°
  • -90° to 90°
  • 0° to 90° (correct)
  • 0° to -90°
  • What is the purpose of reference angles in trigonometry?

  • To find the angle of depression
  • To find the trig values of non-acute angles (correct)
  • To find the complementary angles
  • To find the coterminal angles
  • What is the relationship between coterminal angles?

  • They differ by a multiple of 360° (correct)
  • They differ by a multiple of 90°
  • They sum up to 180°
  • They sum up to 90°
  • What is the characteristic of angles of depression?

    <p>They are always negative</p> Signup and view all the answers

    What is the sum of complementary angles?

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

    How can you find the reference angle of an angle in QII?

    <p>By subtracting the angle from 180°</p> Signup and view all the answers

    If a building is 50 meters tall, and the angle of elevation from a point on the ground to the top of the building is 60°, what is the distance from the point to the base of the building?

    <p>40 meters</p> Signup and view all the answers

    An angle of depression is always greater than its corresponding angle of elevation.

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

    What is the reference angle of an angle of 135° in standard position?

    <p>45°</p> Signup and view all the answers

    Two angles are complementary if their sum is ________________________.

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

    Match the following angles with their descriptions:

    <p>Angle whose measure is between 0° and 90° = Angle of elevation Angle whose measure is between 90° and 180° = Angle of depression Angle whose measure is between 0° and 360° = Coterminal angle Angle formed by a horizontal line and a line of sight below the horizontal = Angle of depression</p> Signup and view all the answers

    Study Notes

    Trigonometric Angles

    Angles of Elevation

    • An angle of elevation is the angle between the line of sight and the horizontal when the object is above the horizontal.
    • It is the angle between the observer's line of sight and the horizontal when looking up at an object.
    • Angles of elevation are always positive (0° to 90°).

    Angles of Depression

    • An angle of depression is the angle between the line of sight and the horizontal when the object is below the horizontal.
    • It is the angle between the observer's line of sight and the horizontal when looking down at an object.
    • Angles of depression are always negative (0° to -90°).

    Reference Angles

    • A reference angle is the acute angle (less than 90°) formed by the terminal side of an angle and the x-axis.
    • Reference angles are used to find the trig values of non-acute angles.
    • Reference angles can be found by subtracting the angle from 180° (if the angle is in QII) or by subtracting the angle from 360° (if the angle is in QIII or QIV).

    Coterminal Angles

    • Coterminal angles are angles that have the same terminal side.
    • Coterminal angles differ by a multiple of 360°.
    • Examples: 30° and 390° are coterminal angles because 390° - 30° = 360°.

    Complementary Angles

    • Complementary angles are two angles whose sum is 90°.
    • If the angles are x and y, then x + y = 90°.
    • Examples: 30° and 60° are complementary angles because 30° + 60° = 90°.

    Trigonometric Angles

    Angles of Elevation

    • Angle between the line of sight and the horizontal when the object is above the horizontal
    • Always positive (0° to 90°)
    • Formed when looking up at an object

    Angles of Depression

    • Angle between the line of sight and the horizontal when the object is below the horizontal
    • Always negative (0° to -90°)
    • Formed when looking down at an object

    Reference Angles

    • Acute angle (less than 90°) formed by the terminal side of an angle and the x-axis
    • Used to find the trig values of non-acute angles
    • Found by subtracting the angle from 180° (if in QII) or from 360° (if in QIII or QIV)

    Coterminal Angles

    • Angles that have the same terminal side
    • Differ by a multiple of 360°
    • Examples: 30° and 390° are coterminal angles because 390° - 30° = 360°

    Complementary Angles

    • Two angles whose sum is 90°
    • If angles are x and y, then x + y = 90°
    • Examples: 30° and 60° are complementary angles because 30° + 60° = 90°

    Trigonometric Angles

    Angles of Elevation

    • Formed when the object is above the horizontal
    • Measured between the line of sight and the horizontal
    • Always positive, ranging from 0° to 90°

    Angles of Depression

    • Formed when the object is below the horizontal
    • Measured between the line of sight and the horizontal
    • Always negative, ranging from 0° to -90°

    Reference Angles

    • Acute angle formed by the terminal side of an angle and the x-axis
    • Used to find trig values of non-acute angles
    • Found by subtracting the angle from 180° (QII) or 360° (QIII or QIV)

    Coterminal Angles

    • Angles with the same terminal side
    • Differ by a multiple of 360°
    • Examples: 30° and 390° are coterminal angles because 390° - 30° = 360°

    Complementary Angles

    • Two angles whose sum is 90°
    • If the angles are x and y, then x + y = 90°
    • Examples: 30° and 60° are complementary angles because 30° + 60° = 90°

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    Description

    Learn about angles of elevation and depression, including their definitions and how they are measured. Understand the differences between these two types of trigonometric angles.

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