precalc final

Question 1

What is the formula for arc length?

Answer 1

s = r0, where s is arc length, r is radius, 0 is in radians. (also: 0 = s/r)

Question 2

How do you find the coordinates on a circle with radius r and angle 0?

Answer 2

(x,y) = rcos0,rsin0

Question 3

One full circle revolution is ___ radians

Answer 3

2pi

Question 4

btw memorize some unit circle stuff

Answer 4

ok

Question 5

to get radius and angle from a terminal ray intersecting a circle of radius r at the given point

Answer 5

r = sqrt(x^2 + y^2) 0 = tan^-1(y/x). Adjust angle by adding pi if on quadrant II or III, add nothing if on quadrant I, and add 2pi if on quadrant IV

Question 6

will you review sin and cos graphs for the exam?

Answer 6

yea

Question 7

how to get period and frequency?

Answer 7

period = 2pi/b, frequency = 1/period

Question 8

What is amplitude?

Answer 8

Half the dist between max and min

Question 9

for tan(2θ), the period and vertical asymptote is

Answer 9

period: pi/b, v. asymptote: pi/2b + k pi/b where k is any integer

Question 10

petals will be oriented on the x and y axis if they are

Answer 10

cos petals

Question 11

csc and sec graphs will be

Answer 11

parabolas facing away from the curves

Question 12

polar to rectangular

Answer 12

x = rcos0, y = rsin0

Question 13

rectangular to polar (where 0 < theta < 2pi)

Answer 13

sqrt(x^2+y^2), tan^-1(y/x)

Question 14

polar complex to polar

Answer 14

sqrt(x^2+y^2), tan^-1(y/x)

Question 15

polar complex to rectangular

Answer 15

x = rcos0, y = rsin0

Question 16

petals on cos will open ___, petals on sin will open ___

Answer 16

directly right, right-down

Question 17

circle with cos will open ___, circles with sin will open ___

Answer 17

horizontally, vertically

Question 18

if ___ is odd for a petal equation, it will have 2n petals (___(n0)), and the cycle will become 0, 2pi instead of 0, pi

Answer 18

cos

Question 19

(a +_ bcos(0)) a cardoid (heart shaped circle) is formed when

Answer 19

a = b

Question 20

(a +_ bcos(0)) a dimpled cardoid (egg shaped circle) is formed when

Answer 20

a > b

Question 21

(a +_ bcos(0)) an inner loop limacon (smaller circle inside) is formed when

Answer 21

a < b

Question 22

in stuff “find all solutions for this sin on 0 <_ x <2 pi”, you must

Answer 22

Isolate the sin/cos, find the 2 places where sin is that fraction on the unit circle, and add the corresponding pi

Question 23

the base domain and range of an arcsin graph is:

Answer 23

Domain: -1, 1
Range: -π/2, π/2

Question 24

how do you do stuff like sin(A-B) where x and y are things like pi/2 and 5pi/6 from the unit circle

Answer 24

sin or cos (a + or - b)