YOU HAVE 20 MINUTES…

Pick up everything you need off the back desk to finish the practice test from yesterday.

Make sure your scan tron has your name on it.

Check your Unit 5 homework also!

TRIG

ONOMETRY

M

AR

Y

LA

UR

EN

W

IL

LI

S

SY

DN

EE

W

IL

CH

ER

KA

YL

EE

S

.

KA

YL

A

S.

PERIODIC FUNCTIONS

Periodic Function- repeats a pattern of y-values at regular intervals

Period- horizontal length of one cycle

Cycle-one complete pattern

Amplitude- height; measures variations in the function values

½(Maximum-Minimum)

Amplitude deals with the ___ value.

Period deals with the ___ value.

1). Highlight one cycle2). Period?3). Amplitude?4). Graph the midline

UNIT CIRCLE

EXAMPLES

Convert measure to radians or degrees:

1. 260°

2. -220°

3. 5π/4

4. -6π/5

HOW TO GRAPH TRIGONOMETRIC FUNCTIONSy= asin b(x-c)+d

y= acos b(x-c)+d

• a= amplitude• If negative- flip

• b= period

• c= horizontal shift

• d= vertical shift

SINE AND COSINE GRAPHS

Graph sinΘ and cosΘ

Period= 2πAmplitude=1

~amplitude and period correspond~

SHIFTING SINE AND COSINE GRAPHS

Shift y=sin(x) π/2 units right

Equation:

TRANSFORMATIONS

y=2cosΘ

Domain:

Range: Amplitude:

Period:

Phase Shift:

Vertical Slide:

GRAPH TANGENT

Domain:

Range: Amplitude:

Period:

Zeroes:

y=tanΘ

TRIGONOMETRIC EQUATIONS

• a impacts the amplitude of the graph

• b alters the period

• A change in c causes a horizontal shift• When c is positve(x-c), the graph shifts right• When c is negative(x+c), the graph shifts left

• A change in d causes a vertical shift• When d is positive, the graph shifts up• When d is negative, the graph shifts down

TRIG IDENTITIES- RECIPROCAL IDENTITIES

Tangent Sin/Cos or Y/X

Cosecant 1/Sin or 1/Y

Secant 1/Cos or 1/X

Cotangent Cos/Sin or X/Y

TRIG IDENTITIES- PYTHAGOREAN IDENTITIES

CosΘ+ Sin²Θ=1

1+Tan²Θ= sec²Θ

1+Cot²Θ= csc²Θ

VERIFY TAN²Θ- SIN²Θ= TAN²ΘSIN²Θ

SIMPLIFY (1+COT²Θ)(SEC²Θ-1)

UNIT 6 QUESTIONS

UNIT 6 QUESTIONS