4.2 / 4.3 pre calc quiz

Ace your homework & exams now with Quizwiz!

input of t angle, cos t outputs....

'x' length of intersection

input of t angle, sin t outputs....

'y' height of intersection

120 degrees, 2π/3

(-1/2, √3/2)

135 degrees, 3π/4

(-√2/2, √2/2

150 degrees, 5π/6

(-√3/2, 1/2)

90 degrees, π/2

(0, 1)

60 degrees, π/3

(1/2, √3/2)

45 degrees, or π/4

(√2/2, √2/2)

30 degrees, or π/6 coordinate

(√3/2, 1/2)

sec t =

1/x; x can't be 0

cdc t =

1/y; y can't be 0

Cofunctions

A trigonometric function whose value for the complement of an angle is equal to the value of a given trigonometric function of the angle itself <the sine is the cofunction of the cosine> For ex, the sin of one angle is equal to the opp/hyp, while the cos of the other angle is equal to the adj/hyp, or the same exact ratio so the cos of theta= sin(90-theta)

If cotθ=1/4 and tan(π/2-θ)

Cotθ=tan(90-θ) 1/4=π/2 - θ 1/4 = definition

cosine domain and range:

D: (-inf, inf) all real numbers R: [-1, 1]

sine domain and range

D: (-inf, inf) all real numbers R: [-1, 1]

Cofunction identities

Sinθ=cos(90-θ) Tanθ=cot(90-θ) Secθ=csc(90-θ) Cosθ=sin(90-θ) Cotθ=tan(90-θ) Cscθ=sec(90-θ)

odd functions

algebra: when you input -x into a function, you get the opposite function out graphically: end behavior is going opposite way, point symmetry

even functions

algebra: when you input -x into a function, you get the same function out graphically: end behavior is going same way, symm in y-axis

pythagorean identities (3) ***

all stemmed from x^2 + y^2 = 1 -plug in sin and cos for x and y in OG and use reciprocal identities to replace OG: sin^2 t + cos^2 t = 1 1 + tan^2 t = sec^2 t 1 + cot^2 t = csc^2 t going to be pos/neg because of square root so look where it is (I II II or IV quad) to eliminate pos/neg value solving for

quotient identities (2)

combines all into 2 equations tan t = sin t / cos t cot t = cos t / sin t

trigonometric identities

equations that are always true for all real numbers for which the trigonometric function is defined

sec (-t) = sec(t)

even

cos (-t) = cos(t)

even function because if you put in a negative angle, you get the same as a positive angles output

reciprocal identities (6) sin cos tan csc sec cot

just plugging in trig terms for x and y sin t= 1/csc t cos t= 1/sec t tan t = 1/cot t csc t = 1 /sin t sec t = 1/cos t cot t= 1/tan t

unit circle angles for 30,60,90

legs: opp 30 deg: 1/2, opp 60 deg: √3/2 hyp: 1

unit circle angles for 45,45,90

legs: √2/2, √2/2 hyp: 1

cot (-t) = -cot

odd

csc (-t) = -csc t

odd

sin (-t) = -sin t

odd

tan (-t) = -tan t

odd

periodic properties of sin and cos

sin (t + 2pi) = sin t cos (t + 2pi) = cos t *both have period 2pi, so just be neg if not multiple of 2pi

periodic properties of tan and cot

tan (t + pi) = tan t cot (t + pi) = cot t *both have period pi, so just

cos t =

x

cot t =

x/y; y can't be 0

how to prove on unit circle ? (formula)

x^2 + y^2 = 1

sin t =

y

tan t =

y/x; x can't be 0


Related study sets

Anatomy Quiz #3: Bones and Bone Markings

View Set

CSCI 207, COP1220 Final, Midterm, Computer Programming 1500 Final

View Set

Tema 1 La crisis del Antiguo Régimen, Tema 7: La Segunda Guerra Mundial, Tema 6 La época de entreguerras (1919 - 1939), Tema 5. Imperialismo, guerra y revolución, Tema 3: La Revolución Industrial y los cambios sociales, Tema 2: Revoluciones liberales...

View Set

Blood Bank - Serologic and Molecular Testing

View Set

Leadership Midterm Case Study 7: Spinal Cord Injury

View Set

Midcourse Content Exam PDBIO 210

View Set