Sinusoid Properties For Pre-Calc

Some sinusoid parent properties, mainly tan, sec, csc, and cot

Domain of Tangent

{x|x doesn’t equal pi/2 +pi(k)}

Period of tangent

pi

Range of Tangent

(- infinity - infinity)

Asymptotes of tangent

{x|x= pi/2 + pi(k)

What graph is this?

Tangent

F(x)>0 Tangent

(0 + pi(k), pi/2 +pi(k))

f(x)

(-pi/2 + pi(k), pi/2 + pi(k))

Increasing Tangent

(-pi/2 + pi(k), pi/2 + pi(k))

Decreasing Tangent

N/A

Concave Up Tangent

(0 + pi(k), pi/2 + pi(k))

Concave Down Tangent

(-pi/2 + pi(k), 0 + pi(k))

Tangent Pattern

ADIUA

Domain Cosecant

{x|x doesn’t equal 0+ pi(k)}

Range Cosecant

(- infinity, -1\] U \[1, infinity)

Period Cosecant

2pi

Is Cosecant odd or even

odd

Cosecant Pattern

AUADA

Which Graph is this

Cosecant

Is Cosine Odd or even

even

Is secant odd or even

even

Domain Secant

{x|x doesn’t equal pi/2+ pi(k)}

Range Secant

(-infinity - infinity\] U \[1, infinity)

Period Secant

2 pi

Pattern Secant

UADAU

What Graph is this?

Secant

Domain of Cotangent

{x|x doesn’t equal 0+ pi(k)}

Range of Cotangent

(-infinity - infinty)

Period of Cotangent

pi

Is Cotangent odd or even

odd

Asymptotes of Cotangent

{x| x=0 + pi (k)}

Pattern Cotangent

AUIDA

What graph is this

Cotangent

Is sin odd or even

odd

What is the inverse of period

Frecuency

What is a sinusoid

A smooth oscillating curve that continues forever