Analysis & Approaches

Trigonometry & Geometry

Contents: Click to skip to subtopic

3.1

3.2

  triangles  

3.3

Trig. applications

3.4

3.5

3.6

  identities  

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

3.15

3.16

3.17

  planes (HL)  

3.18

intersecting planes (HL)

 

3.1: 3D Geometry

 

3.2: SOHCAHTOA & triangle rules

 

3.3: Trigonometric applications

 

3.4: Arcs & sectors + radians

 

3.5: Unit circle and exact values

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
Answer
Answer
Answer
Answer
 

3.6: Trigonometric identities

 

3.7: Trigonometric graphs

Video

 

3.8: Solving trigonometric equations

Video

Exercises

Solutions

Standard Level content

 

3.9: Reciprocal trigonometric ratios [AHL]

Additional Higher Level content

 

3.10: Compound angle formula [AHL]

 

3.11: Other trig properties [AHL]

 

3.12: Vector basics [AHL]

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
Answer
Answer
Answer
 

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

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
Answer
Answer
Answer
 

3.14: Vector equations of lines [AHL]

 

3.15: Intersections of lines [AHL]

 

3.16: Vector product [AHL]

 

3.17: Planes [AHL]

 

3.18: Intersections of planes [AHL]

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