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