you have 20 minutes…
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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
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PERIODIC FUNCTIONSPeriodic Function- repeats a pattern
of y-values at regular intervalsPeriod- horizontal length of one cycleCycle-one complete patternAmplitude- height; measures
variations in the function values½(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
EXAMPLESConvert measure to radians or degrees:
1. 260°2. -220°3. 5π/44. -6π/5
HOW TO GRAPH TRIGONOMETRIC FUNCTIONSy= asin b(x-c)+dy= 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 TANGENTDomain:
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
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