5.3 Trigonometric Functions of Any Angle; Unit Circle

cot x and csc x (Pythagorean Identities)

1 + cot² x = csc² x

(x,y)

(cosθ, sinθ)

tan x and sec x (Pythagorean Identities)

1 + tan² x = sec² x

sec x= (Reciprocal Identities)

1/cosx

tan x= (Reciprocal Identities)

1/cotx

sin x= (Reciprocal Identities)

1/cscx

cos x= (Reciprocal Identities)

1/secx

csc x= (Reciprocal Identities)

1/sinx

cot x= (Reciprocal Identities)

1/tanx

sec(θ)= (graph)

r/x x≠0

csc(θ)= (graph)

r/y y≠0

tan x= (Quotient Identities)

sin x/cos x

cos x and sin x (Pythagorean Identities)

sin² x + cos² x = 1

Quadrant 1 (QI)

ALL are positive (+,+)

Quadrant 4 (QIV)

All are negative DESPITE cosθ and secθ (+,-) sinθ<0 cosθ>0 tanθ<0 cscθ<0 secθ>0 cotθ<0

Quadrant 2 (QII)

All are negative DESPITE sinθ and cscθ (-,+) sinθ>0 cosθ<0 tanθ<0 cscθ>0 secθ<0 cotθ<0

Quadrant 3 (QIII)

All are negative DESPITE tanθ and cotθ (-,-) sinθ<0 cosθ<0 tanθ>0 cscθ<0 secθ<0 cotθ>0

cot x= (Quotient Identities)

cos x/sin x

cos(θ)= (graph)

x/r

cot(θ)= (graph)

x/y y≠0

sin(θ)= (graph)

y/r

tan(θ)= (graph)

y/x x≠0