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Questions and Answers
What is the range of angles of elevation?
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?
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?
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?
What is the characteristic of angles of depression?
What is the sum of complementary angles?
What is the sum of complementary angles?
How can you find the reference angle of an angle in QII?
How can you find the reference angle of an angle in QII?
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?
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?
An angle of depression is always greater than its corresponding angle of elevation.
An angle of depression is always greater than its corresponding angle of elevation.
What is the reference angle of an angle of 135° in standard position?
What is the reference angle of an angle of 135° in standard position?
Two angles are complementary if their sum is ________________________.
Two angles are complementary if their sum is ________________________.
Match the following angles with their descriptions:
Match the following angles with their descriptions:
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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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