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