math

Whenever YOU take the square root of something you need to

account for positive and negative

log and exponential relationship

log_b(x)=a , B^a=x

reference angle is the

angle from terminal side to x-axis

coterminal angle how to find

add 2 pi or 360 or subtract these values to find an angle that will have a coterminal side in the same position

where are the multiples of 60, 30, and 45 located on the unit circle

the multiples of 30 are closest to the x-axis, the multiples of 60 are closest to the y-axis, and the multiples of 45 are in the middle.

what are the coordinates of the x and y axis on the unit circle

x-axis is (1,0) and y is (0,1)

first quadrant special angles (in order, degrees, radians, coordinates)

30, pi/6, (√3/2, 1/2)
45, pi/4, (√2/2, √2/2)
60, pi/3, (1/2, √3/2)

since tangent is rise over run (sin/cos) or slope, that means the tangent of the y and x axes are

x-axis, 0 HOY (horizontal, zero, y=)
y-axis, DNE VUX (vertical, undefinied, x=)

when an angle is plotted in standard position on a non-unit circle, the sine and cosine are

y/r or x/r

what are the standard right triangle trig functions

SOH CAH TOA
sine - opposite/hypotenous
cosine - adjacent/h
tangent- opp/adj

reference angle is always a distance so it is always

positive

how to convert degrees to radians

multiply angle by pi/180

reciprocal identities

csc = 1/sin
sec = 1/cos
cot = 1/tan or cos/sin

even and odd identities

sin (-x) = -sin (x) , cos (-x) = cos (x) , tan(-x) = -tan(x)

pythagorean identities

sin² + cos²= 1
tan²+ 1 = sec²
1 + cot²= csc²

a primary cycle has how many points

5

what is the shape of a standard sine function

a wave that starts at the midline, peaks at max, midline, dips at min, midline

what is the standard shape of a cos function

a u shape that starts at the max, mid, min, mid, max

equation for midline

max + min/2

equation for amplitude

max - min / 2

period equation

end point - starting point

what is the phase shift

the starting x-value

what is the sin or cos function equation and what does each letter represent

y = Asin(Bx + C) +D
|A| = amplitude, sign depends on type of graph pos or negative
Period = 2pi/B
Phase shift = -C/B
D = midline

steps for finding equation from given sine or cos graph

1. identify the type of graph (sine/cos) (pos/neg) visually

2. identify the max/min and start/end points visually

3. identify midline (max + min/2) = D

4. amplitude (max - min/2) = |A|

5. period (end point - starting point) = 2pi/B

6. Phase shift = starting point = -C/B

7. equation

how to identify point spacing

period/4 or period x 1/4

your point spacing shows you what each x-value should be, you can check it because the end - starting =

period

steps for drawing graph given equation

1. Establish shape from given characteristics (type of graph: pos/neg, sine/cos)

2. Identify and draw midline = D

3. Identify the amplitude = |A|

4. find the max and min by adding/subtracting the amplitude to the midline value

5. identify the phase shift (starting point) -c/b

6. period 2pi/B

7. point spacing period/4

how to restrict function from equation

in quadratics, the vertex is at h=x, which is where the turning point will be. If not plug in points and find turning points so its all positive or all negative.