The document outlines key concepts in trigonometry, including ratios and identities, trigonometric equations, and properties related to triangles. It discusses angle measurement systems in both British (degrees) and French (grades), as well as radian measurement, along with the behavior of trigonometric ratios in different quadrants. Additionally, various proofs and working rules for trigonometric functions are presented.

1. TRIGONOMETRY
# Phase I: Ratios & Identities
# Phase II: Trigonometric Equation
# Phase III: Properties of Triangle
Ratio & Identities
Problem: Show that:
1. =
2. = ±
Extended definition of Trigonometric Function [Circular Function]
In cycle of unity raids sine all
= x(-, +) P(x, y) (+, +)
= y r=1
=
(-, -) (+, -)
tangent cosine
Convention:
i) If θ is measured in anticlockwise then it is assume positive.
ii) If θ is measured in clockwise then it is assume negative.

2. Angle MeasurementsSystem
(i) British System (Degree)
Right angle = 90°
1° = 60 min
1min = 60sec
e.g.: 43°23’37”
(ii) French System (grades)
Right angle =
= 100 min
1min = 100sec
e.g.: 63’97”
(iii) Circular System
Right angle = radian
e.g.:
NOTE: - If nothing is mentioned, consider it to be in radians.
T-Ratios of Allied Angles: (90°±θ,180°±θ, 270°±θ etc.)
= p”xP(x,y)
Proof: 90°-θ
= x yy
In ΔOPP”;θ
= x P’
⇒ = x
⇒ =
Working Rule:
Step1: First of all decide sing of T-Ratio from which quadrant is sutatute.
e.g.:180°+θ is in third quadrant where θ∈R
Step2: #If n is even ⇒ NO CHANGE
#If n is odd then interchanges as follows
sin ⟷ cos
tan ⟷ cot
sec ⟷ cosec
Problem: Prove that:
i) = -1
ii) = 0

3. iii) = 0
iv) +