Midterm review 2

Log_b(x) = y (exponential form) (equal other way too)

b^y = x

Requirements for Log_b(x) = y

b > 0, b can’t equal 1

What is the domain of the log function with base b? (Log_b(x) = y)

(0, infinity)

What is the range of the log function with base b? (Log_b(x) = y)

(-infinity, infinity)

What is the default base for a log with no base shown (y = log(x))

10

What is log_e(x) the same as?

ln(x)

what is y = ln(x) the same as (can be written the other way too)

e^y = x

log_b(bⁿ) is equal to assuming that n > 0… (10^log(32) = 32)

n

log_b(MN) is equal to… (cannot use other way around)

log_b(M) + log_b(N)

log_b(M/N) is equal to… (cannot use other way around)

log_b(M) - log_b(N)

log_b(M) in change-of-base formula

log_n(M) / log_n(b)

log_b(M) in more ways of change-of-base formula

log(M) / log(b) and ln(M) / ln(b)

log_b(M) = log_b(N) in one-to-one property formula (interchangable)

M = N

What is terminal side of an angle

The ray where the angle’s rotation ends

What is 90 degrees in radians?

π / 2

What is 60 degrees in radians?

π / 3

What is 45 degrees in radians?

π / 4

What is 30 degrees in radians?

π / 6

What is 0 degrees in radians?

2π

What is 180 degrees in radians?

π

What are coterminal angles?

2 angles in standard position that have the same terminal side

What is a reference angle?

the size of the smallest acute angle formed by the terminal side of the angle and the horizontal axis

What is 270 degrees in radian measure

3π/2

what is cos(Ø) in the (x,y) graph

x

what is sin(Ø) in the (x,y) graph

y

Pythagorean Identity

(cosØ)² + (sinØ)² = 1 or x² + y² = 1²

tan(Ø) is equal to…

sin(Ø)/cos(Ø) or y/x

csc(Ø) is equal to…

1/sin(Ø) or 1/y

sec(Ø) is equal to…

1/cos(Ø) or 1/x

cot(Ø) is equal to…

1/tan(Ø) or 1/(sin(Ø)/cos(Ø))) or x/y

Reciprocal of Sine

Cosecant

Reciprocal of Tangent

Cotangent

Reciprocal of Cosine

Secant

Quadrant II characteristics

Sine and cosecant is positive

Quadrant I characteristics

All trigonometric functions are positive

Quadrant III characteristics

Tangent and cotangent is positive

Quadrant IV characteristics

Cosine and secant is positive

sin(90), cos(90), tan(90)

1, 0, DNE

sin(0), cos(0), tan(0)

0, 1, 0

sin(180), cos(180), tan(180)

0, -1, 0

sin(270), cos(270), tan(270)

-1, 0, DNE

sin(360), cos(360), tan(360)

0, 1, 0

Right Triangle Relationships (sin)

opposite/hypotenuse

Right triangle relationships (cos)

adjacent/hypotenuse

Right triangle relationships (tan)

opposite/adjacent

Reciprocal Right Triangle relationships (csc)

hypotenuse/opposite

Reciprocal Right Triangle relationships (sec)

hypotenuse/adjacent

Reciprocal Right Triangle relationships (cot)

adjacent/opposite