YOU HAVE 20 MINUTES Pick up everything you

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!

Y R T E M O L L I W R N E E H R C U IL A W L E S. Y E R N E. A M YD LE S S AY LA K AY K R T N O IG IS

PERIODIC FUNCTIONS Periodic Function- repeats a pattern of yvalues 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: 1. 260° 2. -220° 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 sinΘ 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 Domain: Range: Amplitude: Period: Phase Shift: y=2 cosΘ 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 1+Tan²Θ= sec²Θ 1+Cot²Θ= csc²Θ

VERIFY TAN²Θ- SIN²Θ= TAN²ΘSIN²Θ

SIMPLIFY (1+COT²Θ)(SEC²Θ-1)

UNIT 6 QUESTIONS

UNIT 6 QUESTIONS