appc 9-14

radian

1 radius

To convert radians to degrees

180/ pi

To convert degrees to radians

pi/180

Length of a circular arc

s=r theta

linear speed

arc length / time

angular speed

central angle / time

sin theta

opp/hyp

cos theta

adj / hyp

tan theta

opp/adj

cot theta

adj/opp

csc theta

hyp / opp

sec theta

hyp / adj

Quotient Identity tan u

sin u / cos u

Quotient identity cot u

cos u / sin u

Pythagorean identities

sin2 u + cos2 u = 1

1 + tan2 u = sec2 u

1 + cot2 u = csc2 u

30-60-90 triangle

1) Hypotenuse is 2 time short leg

2) Long leg is 3 times short leg

45-45-90 triangle

1) Hypotenuse is 2 times leg

2) Two legs are equal

What is “All Students Take Calculus” used for?

Memory aid to remember what

quadrants sine, cosine, tangent are

positive in.

Q1 – all, Q2 sin,csc, Q3 tan,cot, Q4

cos,sec

Reference angle

The angles between 0 and 90 degrees

that can be used to determine all of the

other quadrant angles

sine curve

The plotting of the heights of the y-

values of a point as the point moves

counter-clock wise around a circle

cosine curve

The plotting of the lengths of the x-

values of a point as the point moves

counter-clock wise around a circle

amplitude

Half the distance between the minimum

and maximum y-values of the sine or

cosine curve. Given by |a|.

period

The distance along the x-axis required

for a trig function to obtain all of the

values of its range. 𝑃𝑒𝑟𝑖𝑜𝑑 = 2 pi/b

polar coordinate system

Two-dimensional coordinate system in

which each point on a plane is

determined by a distance from a

reference point and an angle from a

reference direction.

pole

The origin in the polar coordinate

system

polar axis

The positive x-axis in the polar

coordinate system

polar coordinates

A pair of coordinates locating the

position of a point in a plane, the first

being the length of the straight line ( r )

connecting the point to the origin, and

the second the angle ( θ ) made by this

line with a fixed line.