Trigonometric

Functions Review

The test is tomorrow! You

will do awesomely! Yay!

Exam

ple

1:

Rolle

r Coa

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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

w Al

l To

geth

er

Amplitude = 3Period = 360/2 = 180ºPrincipal Axis: y = 2

Amplitude PeriodClue

PrincipalAxis

Exit

Slip

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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

dow

(cal

c.)

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

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on y

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Grap

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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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Win

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(cal

c.)

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

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r (de

gree

s)

Exit

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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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Win

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(cal

c.)

Xmin = 0, xmax = 360, xscl = 90Ymin = -5, ymax = -1, yscl = 1

Y1 = -2cos(x) – 3Y2 = -2

2nd-Trace-Intersect

Dete

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(cal

c.)

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