Learning...
In this lesson you will learn how to use the fundemental tring identities to simplfy trigonometric identities!
TRIG IDENTITIES
TRIG IDENTITIES
Reciprocal Identities
sin θ = 1 csc θ = 1
csc θ sin θ
cos θ = 1 sec θ = 1
sec θ cos θ
tan θ = 1 cot θ = 1
cot θ tan θ
The s functions (sin and secant) are the reciprocals of the c functions (cosecant and cosine)
sin θ = 1 csc θ = 1
csc θ sin θ
cos θ = 1 sec θ = 1
sec θ cos θ
tan θ = 1 cot θ = 1
cot θ tan θ
The s functions (sin and secant) are the reciprocals of the c functions (cosecant and cosine)
Pythagorean Identities
sin²θ + cos²θ = 1
sin²θ = 1 − cos²θ.
cos²θ = 1 − sin²θ.
1 + tan²θ = sec²θ
1 + cot²θ = csc ²θ <--------------- Remember: the "co"s go together. (cotangent and cosecant)
sin²θ + cos²θ = 1
sin²θ = 1 − cos²θ.
cos²θ = 1 − sin²θ.
1 + tan²θ = sec²θ
1 + cot²θ = csc ²θ <--------------- Remember: the "co"s go together. (cotangent and cosecant)
Even/Odd Identities
sin (–x) = –sin x cos (–x) = -cos x
tan (–x) = –tan x cot (–x) = –cot x
sec (–x) = sec x csc (–x) = –csc x
sin (–x) = –sin x cos (–x) = -cos x
tan (–x) = –tan x cot (–x) = –cot x
sec (–x) = sec x csc (–x) = –csc x
Quotient Identities
tan θ = sin θ cot θ = cos θ
cos θ sin θ
tan θ = sin θ cot θ = cos θ
cos θ sin θ
Cofunction Identities
sin(π/2 – x ) = cos x cos (π/2 – x ) = sin x
tan (π/2 – x ) = cot x cot (π/2 – x ) = tan x
sec (π/2 – x ) = csc x csc (π/2 – x ) = sec x
Helpful Hint for Cofunction Identity: Sin goes with cosine,
Tangent goes with cotangent
Secant goes with cosecant
sin(π/2 – x ) = cos x cos (π/2 – x ) = sin x
tan (π/2 – x ) = cot x cot (π/2 – x ) = tan x
sec (π/2 – x ) = csc x csc (π/2 – x ) = sec x
Helpful Hint for Cofunction Identity: Sin goes with cosine,
Tangent goes with cotangent
Secant goes with cosecant
Use each trigonometric identity to simplify
the problem. Evaluate to it's simplest
form. Remember to re-write expressions in terms of sin and cosine.
