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Analysis & Approaches
Trigonometry & Geometry
Contents: Click to skip to subtopic
3.1
3.2
triangles
3.3
Trig. applications
3.5
3.6
3.7
3.10
3.11
3.12
3.13
3.14
3.16
3.17
3.18
intersecting planes (HL)
3.1
3.1: 3D Geometry
3.2
3.2: SOHCAHTOA & triangle rules
3.3
3.3: Trigonometric applications
3.4
3.4: Arcs & sectors + radians
3.5
3.5: Unit circle and exact values
Problems:
-
Find sin(150°):
-
Find cos(3π/4):
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Find sin(-60°):
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Solve x=cos⁻¹(-0.5), for 0<x<360°:
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Solve x=sin⁻¹(√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
3.6: Trigonometric identities
3.7
3.7: Trigonometric graphs
Video
3.8
3.8: Solving trigonometric equations
Video
Exercises
Solutions
Standard Level content
3.9
3.9: Reciprocal trigonometric ratios [AHL]
Additional Higher Level content
3.10
3.10: Compound angle formula [AHL]
3.11
3.11: Other trig properties [AHL]
3.12
3.12: Vector basics [AHL]
Problems:
-
Calculate (2i + 5j) + (4i - 7j):
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Calculate (i + 8j) - 2(3i - j):
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If v = (12i + 5j), calculate |v|:
-
If w = (-i + 2j - 2k), calculate |w|:
Answer
6i - 2j
Answer
-5i + 10j
Answer
13
Answer
3
3.13
3.13: Scalar (dot) product & angles [AHL]
Problems:
-
Calculate (2i + 5j)⋅(4i - 7j):
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Calculate (i - 3j - 2k)⋅(5i + 11j - 9k):
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Find the angle between (i - 3j - 2k) & (5i + 11j - 9k):
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Are (2i + 5j) & (-10i + 4j) parallel, perpendicular or neither?:
Answer
-27
Answer
-10
Answer
100deg. (3sf)
Answer
Perpendicular
3.14
3.14: Vector equations of lines [AHL]
3.15
3.15: Intersections of lines [AHL]
3.16
3.16: Vector product [AHL]
3.17
3.17: Planes [AHL]
3.18
3.18: Intersections of planes [AHL]
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