Unit 9B Trigonometry Notes

Angles of Elevation and Depression

• Angles of Elevation:

  • Angle above the horizontal when looking up.

  • Used to calculate heights of objects.

• Angles of Depression:

  • Angle below the horizontal when looking down.

  • Used to calculate depths of objects.

Trigonometric Ratios

• Soh Cah Toa:

  • Sine (Sin): Opposite/Hypotenuse.

  • Cosine (Cos): Adjacent/Hypotenuse.

  • Tangent (Tan): Opposite/Adjacent.

Sine Law

• Used for non-right-angled triangles.

• Relates the lengths of sides to the sines of their opposite angles.

• Formula: a/sin(A) = b/sin(B) = c/sin(C).

Cosine Law

• Also used for non-right-angled triangles.

• Relates the lengths of sides to the cosine of the included angle.

• Formula:

  • a² = b² + c² - 2bc * cos(A).

  • b² = a² + c² - 2ac * cos(B).

  • c² = a² + b² - 2ab * cos(C).

Unit 6 Special Segments Notes

Perpendicular Bisector

• Divides a segment into two equal parts.

• Creates right angles.

• Intersects at the midpoint.

Altitude

• Perpendicular segment from vertex to opposite side.

• Can be inside, outside, or on the triangle.

Median

• Segment from vertex to midpoint of opposite side.

• Divides triangle into two equal areas.

Angle Bisector

• Divides angle into two equal angles.

• Intersects at the incenter.

Properties

• An Odd Peanut Butter Cup May Contain Apple Butter Instead:

  • Acronym for Angle Bisector, Perpendicular Bisector, Circumcenter, Median, Centroid, Altitude, Incenter.

• Triangle Midsegment Theorem:

  • Midsegment is half the length of the parallel side.

Unit 7 Quads

Specific Types of Quadrilaterals and Their Properties

1. Square:

   • All sides are equal.

   • All angles are right angles.

   • Diagonals bisect each other at right angles.

2. Rectangle:

   • Opposite sides are equal and parallel.

   • All angles are right angles.

3. Parallelogram:

   • Opposite sides are equal and parallel.

   • Opposite angles are equal.

4. Rhombus:

   • All sides are equal.

   • Opposite angles are equal.

5. Trapezoid:

   • One pair of opposite sides are parallel.

   • Non-parallel sides have different lengths.

Unit 11: Area of Geometric Shapes

• Triangles: ½ Bh

• Parallelograms: Bh

• Trapezoids: ½ (b1+b2)h

• Rhombus/Kites: 1/2(d*d)

• Circles: pi r squared

• Polygons: ½ ap

Unit 12 - Surface Area

• Prisms:

• LSA- ph

• TSA- ph + 2b

• Cylinders:

• LSA- 2pi rh

• TSA- 2 pi rh + 2 pi r squared

• Pyramids:

• LSA- ½ pl

• TSA- ½ pl + b

• Cones:

• LSA- pi r l

• TSA- pi r l + pi r squared

• Spheres

• TSA- 4 pi r squared

• 1/2- 3 pi r squared

Volume Formulas:

• Cylinder: V = πr²h

• Prism: V = Bh (B = base area)

• Pyramid: V = (1/3)Bh

• Cone: V = (1/3)πr²h

• Sphere: V = (4/3)πr³

Unit 13 - Circles Notes:

• Arc Length Formula: arc/360 = x/pi d

• Sector Area Formula: arc/360 = x/pi r squared

• Segment Area Formula: sector area - triangle area

• Properties of Radii and Chords: Equal chords have equal arcs

• Properties of Tangents: Tangents from a point are equal in length