Pre-Calculus CPEMr. Van Hise
sin θ = opp / hyp
cos θ = adj / hyp
tan θ = opp / adj
csc θ = hyp / opp
sec θ = hyp / adj
cot θ = adj / opp
y
x
1
•Centered at origin
•Radius is 1 unit
•Arc length on unit circle corresponds exactly to radian measure
(1, 0)
(0, -1)
(-1, 0)
(0, -1)
y
xθ
(x, y) REMEMBER: sin θ = opp / hyp
This diagram represents the sine function on a unit circle
•In a unit circle, the hypotenuse is 1
•The length of the opposite side is represented by the y-coordinate
SO: sin θ = yopposite
hypo
tenus
e
θ
hypo
tenus
e
This diagram represents the cosine function on a unit circley
x
(x, y) REMEMBER: cos θ = adj / hyp•In a unit circle, the hypotenuse is 1
•The length of the adjacent side is represented by the x-coordinate
SO: cos θ = x
adjacent
sin θ = y
cos θ = x
tan θ = y/x
csc θ = 1 / y
sec θ = 1 / x
cot θ = x / y
2
-2
-5
2
-2
-5
2
-2
-5
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