Evaluating Trigonometric Functions (Precalculus Review 3) September 10th, 2015.
Trigonometric Functions Review
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Transcript of Trigonometric Functions Review
Trigonometric
Functions Review
The test is tomorrow! You
will do awesomely! Yay!
Exam
ple
1:
Rolle
r Coa
ster
He
ight
Finding info from the equation5 min lesson, 5 min exit slip!
Ampl
itude
The number in front of sin or cos is the amplitude. If there is no coefficient, it is 1.
Ignore negative/positive sign. Amplitude is distance, so it is always positive.
Amplitude for this equation = 3
Perio
d
The number in front of the x (inside the parentheses) is our clue to the period. If there is no coefficient, the clue number is 1.
To find the period, divide: 360/clue
In this case, we get: 360/2 = 180º
Prin
cipal
Axis
The number added or subtracted is the principal axis – the vertical shift.
We write the principal axis as an equation:
Here, the answer is: Y = 2
Revie
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Amplitude = 3Period = 360/2 = 180ºPrincipal Axis: y = 2
Amplitude PeriodClue
PrincipalAxis
Exit
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1. Write down the:a. Amplitudeb. Periodc. Principal Axis
Answers:Amplitude = 4, Period = 360/3 = 120º, Principal Axis: y = -2
Graphing Sine and Cosine Equations10 min lesson, 8 min exit slip!
Dete
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Win
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You should always be able to answer these 6:
Xmin: 0º (start)Ymin: 2 – 3 = -1Xmax: 360º (finish) Ymax: 2 + 3 = 5Xscl: 90º (always)Yscl: 1
Grap
h it
on y
our
calcu
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Grap
h it
on
pape
r!
You should do the following:• Draw your principal axis• Sketch the min and max lines• Sine starts in the middle, Cos starts at the
maximum
Dete
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Amplitude = 2, Period = 360º, Pr. Axis: y = -3
You should always be able to answer these 6:
Xmin: 0º (start)Ymin: -3 – 2 = -5Xmax: 720º (finish) Ymax: -3+ 2 = -1Xscl: 90º (always)Yscl: 1
Grap
h it
on y
our
calcu
lato
r (de
gree
s)
Exit
Slip
!!! 3
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inut
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1. Sketch the graph of the one above for: 0º ≤ x ≤ 360º !!
Answer Graph:
Solve Trig. Equations5 min lesson, 4 min exit slip!
Dete
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Xmin = 0, xmax = 360, xscl = 90Ymin = -5, ymax = -1, yscl = 1
Y1 = -2cos(x) – 3Y2 = -2
2nd-Trace-Intersect
Dete
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Answers: 120º, 240º
Exit
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1. Solve for x (should have multiple answers) for 0º ≤ x ≤ 360º!
6 Answers: 9.65º, 110º, 130º, 230º, 250º, 350º
Explanation: • I have to give 3 significant figures for each. • Another way: 9.65 and 110º happen in the first cycle. • Because the period is 120º, add 120º to each to get 130º and
230º. • Then add 120º again to each to get 250º and 350º.
Real-Life Trig Problems5 min lesson, 4 min exit slip!
Temperature: Find amplitude, period, pr. Axis and write eq.
Amplitude = (16 – 7)/2 = 4.5Period = 12 monthsPr. Axis: average y: (16 + 7)/2 = 11.5
Depth: Find amplitude, period, pr. Axis and write eq.
1.5 30 4.5Amplitude = ½ the distance between max & minA = (6 – 3)/2 = 1.5
Period = 360/b12 = 360/b B = 30 (check: 12*30 = 360)
Vertical translation = principal axis, the middle (average of max and min)= (6 + 3)/2 = 4.5