Terracotta Institute

Trigonometry: Finding Angles

Allied Angle: Two angles α and β will be allied angle if there sum or difference is multiple of π/2 .
Ex: α ± β = 0, ± π/2 , ± π...etc.

Value of Allied Angles: Sign of Trigonometric functions are depend on quadrant, Trigonometric functions are Sin θ, Cos θ, tan θ, Sec θ, Cosec θ and Cot θ . Sign of trigonometric ratios in quadrants are as follows:

Quadrant System

In books angles are divided in multiple of 180/360 or 90/270, WHY ??

In multiple of 180/360 --> NO CHANGE IN TRIGONOMETRIC FUNCTIONS

In multiple of 90/270 --> ALL TRIGONOMETRIC FUNCTIONS ARE CHANGE

Instead of learning all these methods we can remember only one thing brake an angle in MULTIPLE of 90

For Example Sin1125 degree, then brake 1125 by dividing it 90.
                                                 (n x 90 + θ) or (n x 90 - θ)

division rule

                                Were n is quotient, 1125 is dividend and 90 is divisor.

There are two cases after braking the given angle:

Case 1 If Quotient (n) is Even Number:   Then NO CHANGE

when n is even

Case 2 If Quotient (n) is Odd Number:   The all Trigonometric functions changed as

When n is odd

NOTE: 

1. Sign must be check by the quadrant.
2. All trigonometric functions are periodic functions, If quotient is a multiple of 4                          then we are at starting line.
3. If angle is negative then make it positive first using rule.

                   Sin (-θ) = - Sin θ,  Cos (-θ) = Cos θ    and   tan (-θ) = - tan θ

         Ex: Find the values of the following trigonometric ratios

               i.      a). Sin 315⁰              b).   Cos (- 480⁰)                   c).  Sin (- 1125⁰)

              ii.     a). Cosec 390⁰          b).   tan 270⁰                         c).  Cot 570⁰

             iii.     a). Sin 4530⁰              b).   tan (- 585⁰)                    c).  Cos 3060⁰