7. Trigonometric Functions

Question 1

π^R =

Answer 1

180°

Question 2

Length of arc in circle of radius r and central angle θ

Answer 2

s = rθ

Question 3

Area of sector of circle of radius r and central angle θ

Answer 3

A = 1/2 r²θ

Question 4

tanθ =

Answer 4

sinθ/cosθ

Question 5

cotθ =

Answer 5

cosθ/sinθ

Question 6

cscθ =

Answer 6

1/sinθ

Question 7

secθ =

Answer 7

1/cosθ

Question 8

Graph of…

Answer 8

y = sinx

Question 9

Graph of…

Answer 9

y = cosx

Question 10

Graph of…

Answer 10

y = tanx

Question 11

Graph of…

Answer 11

y = cotx

Question 12

Graph of…

Answer 12

y = secx

Question 13

Graph of…

Answer 13

y = cscx

Question 14

sine

domain and range?

Answer 14

domain: (-∞, ∞)
range: -1 ≤ sinx ≤ 1

Question 15

cosine

domain and range?

Answer 15

domain: (-∞, ∞)
range: -1 ≤ cosx ≤ 1

Question 16

tangent

domain and range?

Answer 16

domain: all real numbers except odd multiples of π/2
range: all real numbers

Question 17

cotangent

domain and range?

Answer 17

domain: all real numbers except all multiples of π
range: all real numbers

Question 18

secant

domain and range?

Answer 18

domain: all real numbers except odd multiples of π/2
range: (-∞, -1] U [1, ∞)

Question 19

cosecant

domain and range?

Answer 19

domain: all real numbers except all multiples of π
range: (-∞, -1] U [1, ∞)

Question 20

General form of a trigonometric function:

y = A • trig(Bx + C) + D

Answer 20

|A| = amplitude

–C/B = horizontal translation

period = period of parent function / B

D = vertical translation

Question 21

Cofunction Identities

(in radians)

Answer 21

trig(x) = cotrig(π/2 – x)

sinx = cos(π/2 – x)

cosx = sin(π/2 – x)

Question 22

Pythagorean Identities

Answer 22

sin²x + cos²x = 1

sec²x = 1 + tan²x

csc²x = 1 + cot²x

Question 23

sin2x =

Answer 23

2(sinx)(cosx)

Question 24

cos2x =

Answer 24

cos²x – sin²x

2cos²x – 1

1 – 2sin²x

Question 25

tan2x =

Answer 25

2tanx / (1 – tan²x)