Angle and its Measurement — Class 11 Maharashtra HSC Mathematics revision notes
A 4-page visual revision sheet for Angle and its Measurement, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Angle and its Measurement in one look
a rotation, not just an opening between two rays
- Initial ray OA: the fixed starting ray, along the positive X-axis in standard position
- Rotation: anticlockwise gives a positive measure, clockwise gives a negative measure
- Terminal ray OB: where it lands decides the angle's quadrant
Directed Angles
- a directed angle AOB is the ordered pair (OA,OB) plus the rotation carrying OA onto OB
- O is the vertex, OA the initial arm, OB the terminal arm
- rotation anticlockwise is positive, rotation clockwise is negative
- zero angle: no rotation at all
- one rotation: a full turn, 360°
- straight angle: half of one rotation, 180°
- right angle: a quarter of one rotation, 90°
Standard Position and Quadrants
- vertex at the origin, initial ray along the positive X-axis: that placement is standard position
- quadrant is decided by where the terminal ray lands, not by the angle's size
- a quadrantal angle's terminal ray sits exactly on an axis: no quadrant at all
Which Quadrant, by Angle
- 0°<θ<90° — quadrant I
- 90°<θ<180° — quadrant II
- 180°<θ<270° — quadrant III
- 270°<θ<360° — quadrant IV
- θ=0°,90°,180° or 270° — quadrantal, terminal ray on an axis, no quadrant
Coterminal Angles
- angles in standard position that share the same terminal ray are coterminal
- two angles are coterminal exactly when their measures differ by an integer multiple of 360°
- that condition in radians: an integer multiple of 360°, that is 2nπ radians, n an integer
- e.g. 30°, 390° and -330° are all coterminal: 390°-(-330°)=720°=2×360°
- to place a large or negative angle, add or subtract 360° repeatedly
- keep going until it lies between 0° and 360°, then read the quadrant
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Angle and its Measurement sheet covers
- Initial ray OA
- Rotation
- Terminal ray OB
- Directed Angles
- Standard Position and Quadrants
- Which Quadrant, by Angle
- Coterminal Angles
- Sexagesimal System (Degree Measure)
- one rotation
- straight angle
- right angle
- minutes and seconds
- Circular System (Radian Measure)
- straight angle in radians
- degree to radian
- radian to degree
- Degree vs Radian
- Degree (sexagesimal)
- Radian (circular)
- Degree to Radian Table
- 0°
- 30°
- 45°
- 60°
- 90°
- 120°
- 180°
- 270°
- 360°
- Why the radian is well defined
- Arc Length
- formula
- Area of a Sector
- Where A = half r squared theta comes from
- Angle between clock hands
- Symbols
- Exterior and Interior Angles of Regular Polygons
- triangle, n=3
- square, n=4
- pentagon, n=5
- hexagon, n=6
- octagon, n=8
- decagon, n=10
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Angle and its Measurement the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.