Unit 4: Trig I

64 terms

0

π÷6

π÷4

π÷3

π÷2

2π÷3

3π÷4

5π÷6

π

7π÷6

5π÷4

4π÷3

3π÷2

5π÷3

7π÷4

11π÷6

360°

an angle measurement that gives the ratio of arc length over radius; makes trig function formulas easy; 57ish degrees

180÷ℵ

ℵ÷180

Sine

ratio of the opposite side to the hypotenuse of a right-angled triangle; percentage of max height; y/r

Cosine

ratio of the adjacent side to the hypotenuse of a right-angled triangle; percentage of max displacement; x/r

Tangent

ratio of the opposite to the adjacent side of a right-angled triangle; slope of radius; y/x

½

√3/2

1/√3

½

½

1

√3/2

½

√3

1

0

Undefined

0

−1

0

−1

0

Undefined

0

1

0

all real numbers

[-1,1]

Domain of Tan

all real numbers except ℵ/2 or ℵn

all real numbers

Reference Angle

measures distance to closest x-axis

Trig Golden Rule

when dealing with sine, radians, cosine or tangent, the size of the circle does not matter, only the size of the angle does

Periodic Function

a function that repeats its pattern of output over a certain length of input (sin, cos, tan, csc, sec, cot)

Period

length of time(input) it takes to complete a cycle of output, after transformation; b

Fundamental Period

how long it takes to complete a full cycle of output

Period Equation

fundamental period ÷ b

Midline

half the max or min; k

Amplitude

distance from a max or min to the midline

2ℵ

Sin Parent Function

Sin(x)=asin(b(x-h))+k

Cos Parent Function

Cos(x)=a(b(x-h))+k

Transform Trig Function Step 1.

Find the Midline(k); (Max-min)/2

TTF Step 2

Find the Amplitude; Measure from max or min to midline

TTF Step 3

Find Period (b); peak to peak, lowest point to lowest point, midline to midline²

TTF Step 4

Pick a place to start function (h); determine if equation is sin or cos