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!

TRIGONOMETRY MARY LAUREN WILLIS SYDNEE WILCHER KAYLEE S. KAYLA 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 cycle 2). Period? 3). Amplitude? 4). Graph the midline

UNIT CIRCLE

EXAMPLES Convert measure to radians or degrees: ° ° 3.5π/4 4.-6π/5

HOW TO GRAPH TRIGONOMETRIC FUNCTIONS y= 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 sin Θ and cosΘ Period= 2π Amplitude=1 ~amplitude and period correspond~

SHIFTING SINE AND COSINE GRAPHS Shift y=sin(x) π/2 units right Equation:

TRANSFORMATIONS y=2cos Θ Domain: Range: Amplitude: Period: Phase Shift: Vertical Slide:

GRAPH TANGENT Domain: Range: Amplitude: Period: Zeroes: y=tan Θ

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

TRIG IDENTITIES- PYTHAGOREAN IDENTITIES 1+Tan² Θ= sec²Θ 1+Cot² Θ= csc²Θ

VERIFY TAN² Θ- SIN²Θ= TAN²ΘSIN²Θ

SIMPLIFY (1+COT² Θ)(SEC²Θ-1)

UNIT 6 QUESTIONS