7. Trigonometric Functions Flashcards
πR =
180°
Length of arc in circle of radius r and central angle θ
s = rθ
Area of sector of circle of radius r and central angle θ
A = 1/2 r2θ
tanθ =
sinθ/cosθ
cotθ =
cosθ/sinθ
cscθ =
1/sinθ
secθ =
1/cosθ
Graph of…
y = sinx
Graph of…
y = cosx
Graph of…
y = tanx
Graph of…
y = cotx
Graph of…
y = secx
Graph of…
y = cscx
sine
domain and range?
domain: (-∞, ∞)
range: -1 ≤ sinx ≤ 1
cosine
domain and range?
domain: (-∞, ∞)
range: -1 ≤ cosx ≤ 1
tangent
domain and range?
domain: all real numbers except odd multiples of π/2
range: all real numbers
cotangent
domain and range?
domain: all real numbers except all multiples of π
range: all real numbers
secant
domain and range?
domain: all real numbers except odd multiples of π/2
range: (-∞, -1] U [1, ∞)
cosecant
domain and range?
domain: all real numbers except all multiples of π
range: (-∞, -1] U [1, ∞)
General form of a trigonometric function:
y = A • trig(Bx + C) + D
|A| = amplitude
–C/B = horizontal translation
period = period of parent function / B
D = vertical translation
Cofunction Identities
(in radians)
trig(x) = cotrig(π/2 – x)
sinx = cos(π/2 – x)
cosx = sin(π/2 – x)
Pythagorean Identities
sin2x + cos2x = 1
sec2x = 1 + tan2x
csc2x = 1 + cot2x
sin2x =
2(sinx)(cosx)
cos2x =
cos2x – sin2x
2cos2x – 1
1 – 2sin2x
tan2x =
2tanx / (1 – tan2x)
