Trigonometric Identities

Reciprocal identities

Quotient Identities

Co-Function Identities

Pythagorean Identities

Sum and Difference Formulas

          

          

Double Angle Formulas

Function	Abbreviation	Description	Trigonometric Identities using Radians
Sine	sin
Cosine	cos
Tangent	tan
Cotangent	cot
Secant	sec
Cosecant	csc

Non-permissible values


Sin x/Cos x                     Cos x cannot be equal to zero

Therefore the non-permissible values of Sin x/Cos x is where Cos x is  equal to zero on the unit circle.

Cos x  is equal to zero at        [    (0,1)    90°    π/2     ]        And       [     (0,-1)     270°    3π/2    ]


general formula for non-permissible values:      X  ≠   π/2 +   πn , n  ∈  I

Tan x/Sec x                     Tan x/Csc x=       Sin x/Cos x / 1/Sin x

 Cos x cannot be equal to zero

 Sin x cannot be equal to zero

Therefore the non-permissible values of   Tan x/Sec x   is where cos x and sin x are equal to zero.

Cos x  is equal to zero at        [    (0,1)    90°    π/2     ]        And       [     (0,-1)     270°    3π/2    ]

Sin x  is equal to zero at        [    (1,0)    0°, 360°   0,2π     ]        And       [     (-1,0)     180°    π   ]

Cos x           X  ≠   π/2 +   πn , n  ∈  I

Sin x            X  ≠   πn , n  ∈  I

general formula for non-permissible values:          X  ≠   π/2n , n  ∈  I

Exact Trigonometric values for angles

2Sinπ/6cosπ/6                  2sin α cos  α  =   sin 2α

 α = π/6           2sin α cos  α =  sin 2π/6

     sin 2π/6= sin π/3 

      sin π/3      Sin 60°                Sin= Opp/Hyp    

 

Exact value:      =    √3 / 2  

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