Analysis & Approaches

Trigonometry & Geometry

Contents: Click to skip to subtopic

3.1

3.2

  triangles  

3.3

Trig. applications

3.5

3.6

  identities  

3.7

3.17

  planes (HL)  

3.18

intersecting planes (HL)

 

3.1: 3D Geometry

pg1 A&A HL - Topic 3 - Trig Notes.jpg
 

3.2: SOHCAHTOA & triangle rules

pg2 A&A HL - Topic 3 - Trig Notes.jpg
 

3.3: Trigonometric applications

pg3 A&A HL - Topic 3 - Trig Notes.jpg
 

3.4: Arcs & sectors + radians

pg4 A&A HL - Topic 3 - Trig Notes.jpg
 

3.5: Unit circle and exact values

pg5 A&A HL - Topic 3 - Trig Notes.jpg

Problems:

  1. Find sin(150°):

  2. Find cos(3π/4):

  3. Find sin(-60°):

  4. Solve x=cos¹(-0.5), for 0<x<360°:

  5. Solve x=sin¹(√3/2), for -π<x<π:

Answer
0.5
Answer
-sqrt2/2
Answer
-sqrt3/2
Answer
  120°,240°  
Answer
 π/3, 2π/3
 

3.6: Trigonometric identities

pg6 A&A HL - Topic 3 - Trig Notes.jpg
 

3.7: Trigonometric graphs

pg7 A&A HL - Topic 3 - Trig Notes.jpg

Video

 

3.8: Solving trigonometric equations

pg8 A&A HL - Topic 3 - Trig Notes.jpg

Video

Exercises

Solving Trig Eqs Worksheet - OWN.jpg

Solutions

Solving Trig Eqs Worksheet - Solutions.j

Standard Level content

 

3.9: Reciprocal trigonometric ratios [AHL]

Additional Higher Level content

pg9 A&A HL - Topic 3 - Trig Notes.jpg
 

3.10: Compound angle formula [AHL]

pg10 A&A HL - Topic 3 - Trig Notes.jpg
 

3.11: Other trig properties [AHL]

pg11 A&A HL - Topic 3 - Trig Notes.jpg
 

3.12: Vector basics [AHL]

pg12 A&A HL - Topic 3 - Trig Notes.jpg
pg13 A&A HL - Topic 3 - Trig Notes.jpg

Problems:

  1. Calculate (2i + 5j) + (4i - 7j):

  2. Calculate (i + 8j) - 2(3i - j):

  3. If v = (12i + 5j), calculate |v|:

  4. If w = (-i + 2j - 2k), calculate |w|:

Answer
  6i - 2j  
Answer
-5i + 10j
Answer
    13    
Answer
      3     
 

3.13: Scalar (dot) product & angles [AHL]

pg14 A&A HL - Topic 3 - Trig Notes.jpg

Problems:

  1. Calculate (2i + 5j)(4i - 7j):

  2. Calculate (i - 3j - 2k)(5i + 11j - 9k):

  3. Find the angle between (i - 3j - 2k& (5i + 11j - 9k):

  4. Are (2i + 5j(-10i + 4j) parallel, perpendicular or neither?:

Answer
    -27   
Answer
    -10    
Answer
100deg. (3sf)
Answer
Perpendicular
 

3.14: Vector equations of lines [AHL]

pg15 A&A HL - Topic 3 - Trig Notes.jpg
pg16 A&A HL - Topic 3 - Trig Notes.jpg
 

3.15: Intersections of lines [AHL]

pg17 A&A HL - Topic 3 - Trig Notes.jpg
 

3.16: Vector product [AHL]

pg18 A&A HL - Topic 3 - Trig Notes.jpg
 

3.17: Planes [AHL]

pg19 A&A HL - Topic 3 - Trig Notes.jpg
pg20 A&A HL - Topic 3 - Trig Notes.jpg
 

3.18: Intersections of planes [AHL]

pg21 A&A HL - Topic 3 - Trig Notes.jpg
pg22 A&A HL - Topic 3 - Trig Notes.jpg
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