4: trig

Question 1

Rules w/ complementary and supplementary angles

Answer 1

Neither complementary nor supplementary angles can be negative

(Angles greater than 90 degrees have no complement, and angles greater than 180 deg have no supplement)

Question 2

Degrees, minutes, seconds relationship

Answer 2

60 seconds in a minute
60 minutes in a degree

Question 3

Angle, radius, and arc length relationship

Answer 3

s = rθ
arc length = radius times angle measure (theta) IN RADIANS

Question 4

Linear speed (and units)

Answer 4

distance/time
AKA (radius)(angular speed)
Units: in/sec, ft/min, etc.

Question 5

Angular speed (and units)

Answer 5

theta/time
units: radians/sec

Question 6

Even functions

Answer 6

Cosine, secant

Question 7

Odd functions

Answer 7

Sine, cosecant, tangent, cotangent

Question 8

Cofunctions of complementary angles

Answer 8

sin(90° - x) = cosx (both ways)
tan(90° - x) = cotx (both ways)
sec(90° - x) = csc x (both ways)
Sin & cos
tan & cot
sec & csc

Question 9

Pythagorean identities

Answer 9

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ

Question 10

Period of parent tangent graph

Answer 10

Pi

Question 11

Arcsin domain

Answer 11

[-1, 1]

Question 12

Arcsin range

Answer 12

[-π/2, π/2]

Question 13

Arccos domain

Answer 13

[1, 1]

Question 14

Arccos range

Answer 14

[0, π]

Question 15

Arctan domain

Answer 15

All real numbers

Question 16

Arctan range

Answer 16

[-π/2, π/2]

Question 17

Period & frequency

Answer 17

Period = time per cycle
Frequency = # of cycles per time
Frequency (f) = 1/period

Question 18

Angular frequency

Answer 18

2π frequency