Exam 1 Formulas and Definitions

Question 1

Complementary angles

Answer 1

add up to 90°

Question 2

Supplementary angles

Answer 2

add up to 180°

Question 3

Coterminal angle formula

Answer 3

β = α + 360°k

Question 4

Radians

Answer 4

Length of the arc of an angle (especially useful on the unit circle)

Question 5

Circumference formula

Answer 5

C = 2πr

Question 6

Conversion factor for radians and degrees

Answer 6

180°/π or π/180°

Question 7

Arc length formula

Answer 7

S = rθ

(for unit circle)

Question 8

Sector area formula

Answer 8

A = (r² θ)/2

Question 9

Angular frequency formula

Answer 9

ω = 2πf

(ω = omega (ex: rad/min))

(f = ordinary frequency = revolution per unit of time)

Question 10

Ordinary frequency formula

Answer 10

f = 1/p

(p = period = time for one revolution (ex: min/rev))

Question 11

Period formula

Answer 11

p = 1/f

(f = ordinary frequency = revolution per unit of time (ex: rev/min))

Question 12

Linear velocity formula

Answer 12

V = rω

(V = r(2π)f)

Question 13

csc(θ)

Answer 13

hyp/opp

(1/sin(θ))

Question 14

sec(θ)

Answer 14

hyp/adj

(1/cos(θ))

Question 15

cot(θ)

Answer 15

adj/opp

(1/tan(θ)) or (cos(θ)/sin(θ))

Question 16

45-45-90 triangle side length examples

Answer 16

1-1-sqrt(2) and (sqrt(2)/2)-(sqrt(2)/2)-1

Question 17

30-60-90 triangle side length examples

Answer 17

1-2-sqrt(3) and (sqrt(3)/2)-(1/2)-1