MATHEMATICS • UNIT 9
Unit 9: Trigonometry – Exact Source Notes
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Source Information
Actual title shown on Page 1: Unit – 9, Trigonometry
Total pages in the uploaded PDF: 221
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Chapter Contents
Typed Source Index
This index types the clearly readable opening definitions and core formulas while the scanned pages below remain the authority for the complete handwritten workings.
Trigonometry – opening notes
Tri – three
Gono – sides or angles
Metron – measurement
Fundamental data: sin θ, cos θ, tan θ
Derived data: cosec θ, sec θ, cot θ
Pythagoras theorem: h² = p² + b²
sin²θ + cos²θ = 1
sec²θ − tan²θ = 1
cosec²θ − cot²θ = 1
sec²θ − tan²θ = 1
cosec²θ − cot²θ = 1
Compound angles
sin(A+B) = sinA cosB + cosA sinB
sin(A−B) = sinA cosB − cosA sinB
cos(A+B) = cosA cosB − sinA sinB
cos(A−B) = cosA cosB + sinA sinB
tan(A+B) = (tanA + tanB)/(1 − tanA tanB)
tan(A−B) = (tanA − tanB)/(1 + tanA tanB)
sin(A−B) = sinA cosB − cosA sinB
cos(A+B) = cosA cosB − sinA sinB
cos(A−B) = cosA cosB + sinA sinB
tan(A+B) = (tanA + tanB)/(1 − tanA tanB)
tan(A−B) = (tanA − tanB)/(1 + tanA tanB)
Multiple-angle formulas shown in the source
sin2A = 2sinA cosA = 2tanA/(1+tan²A)
cos2A = cos²A − sin²A = 1 − 2sin²A = 2cos²A − 1
cos2A = (1 − tan²A)/(1 + tan²A)
tan2A = 2tanA/(1 − tan²A)
sin3A = 3sinA − 4sin³A
cos3A = 4cos³A − 3cosA
tan3A = (3tanA − tan³A)/(1 − 3tan²A)
cos2A = cos²A − sin²A = 1 − 2sin²A = 2cos²A − 1
cos2A = (1 − tan²A)/(1 + tan²A)
tan2A = 2tanA/(1 − tan²A)
sin3A = 3sinA − 4sin³A
cos3A = 4cos³A − 3cosA
tan3A = (3tanA − tan³A)/(1 − 3tan²A)
Conditional trigonometric identities
Definition shown on Page 152: All those identities which are true only under certain condition are known as conditional trigonometric identities.
The source then continues with Exercise 9.4 and later Exercise 9.5.
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Trigonometry Basics
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Compound & Multiple Angles
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Exercise 9.1
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Sub-multiple Angles
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Exercise 9.2
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Exercise 9.3
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Conditional Trigonometric Identities / Exercise 9.4
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Exercise 9.5
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