unit t student success sheet (sss) t sss - math...video and extra problems we will be working out...

Unit T Student Success Sheet (SSS) Graphing Trig Functions (sections 4.5-4.7)

Standards: Trig 4.0, 5.0,6.0

Segerstrom High School -- Math Analysis Honors

© Crystal Kirch 2011

Name: ____________________________________

Period: __________

Thinkbinder Study Group: www.bit.ly/ChatUnitT

Reminders:

Practice Problems (PQ & PT) are completed in spiral bound notebook only.

All pages in spiral notebook should be labeled accordingly:

Unit ______ Concept ______ - (title of assignment) Examples:

Unit T Concept 1 – Practice Quiz Unit T Concept 1-4 – Practice Test

Website with all video links and resources:

kirchmathanalysis.blogspot.com Edmodo Group Codes for class communication:

http://bit.ly/edmodo2013

“Success means having the

courage, the determination,

and the will to become the

person you believe you were

meant to be”

George Sheehan

Concept # What we will be learning… Mandatory

Practice Optional Extra practice

from textbook

1 graphing sine and cosine Practice quiz 1

2 graphing secant and cosecant Practice quiz 2

3 graphing tangent and cotangent Practice quiz 3

This is our final chapter of trigonometry – gosh how time flies! We will conclude our time by graphing the six main trigonometric functions. The blanks on page 2 are the most important things you need to know about trig graphs, so study those carefully! A few websites that will help in your understanding (also linked to on blog in MentorMob Playlist)

http://thinkexist.com/quotation/success_means_having_the_courage-the/163054.html





http://thinkexist.com/quotes/george_sheehan/

---Unit T Student Success Sheet--- Graphing Trig Functions (sections 4.5-4.7)--- Math Analysis Honors---


FINAL GRAPH MUST BE CLEARLY SEEN/LABELED/MARKED...I prefer that you do this in colored pencil so it stands out (NO PEN!). Do

all work in pencil, and once you are sure of your final answer, go over it in color.

Sine/Cosine – I need to see “5 key points”

Cosecant/Secant – I need to see original sine or cosine graph + asymptotes + “1 key point (mountain-top or valley-bottom)

Tangent/Cotangent – I need to see “1 key point” + asymptotes

THINGS TO KNOW ABOUT TRIGONOMETRIC GRAPHS

1. They are ____________________. This means they repeat themselves over and over again. One time through

their cycle is called a ________________________. The end of one period is always the beginning of the next.

When we draw our graphs, I only require you to draw out one period. However, you must know they go on

forever and ever.

2. The period for sine, cosine, cosecant, and secant is _______________________. This means they go through

one cycle while covering _____________ units on the x-axis

3. The period for tangent and cotangent is _______________________. This means they go through one cycle

while covering _____________ units on the x-axis.

4. Cosecant and Secant have asymptotes where sine and cosine are equal to zero. This is because they are the

___________________ of sine and cosine. Thus, if the value of sine is 0, the value of cosecant is 1/0, which is

__________________. Undefined = ______________________________

5. Tangent and Cotangent have asymptotes where their respective ratios are equal to zero. Tangent = sine/cosine,

so when cosine = 0, tangent has asymptotes. Tangent's parent asymptotes are thus at ________ and

__________ (the two points on the unit circle where the “x” value is 0). Cotangent = cosine/sine, so when sine

= 0, tangent has asymptotes. Cotangent's parent asymptotes are thus at ________ and __________ (the two

points on the unit circle where the “y” value is 0).

6. Sine and cosine graphs have an ________________. Amplitudes are ___________ the distance between the

highest and lowest points on the graph. They can be found by looking at the equation at the value of _______.

7. Sine and cosine graphs look like _______________________

8. Cosecant and Secant graphs look like ________________________

9. Tangent and cotangent graphs look like _______________________



WRITING EQUATIONS in graph-able form... [ ( )]

First, You must factor out “b” first!

Then, You must decide how to label your scale on your graph so it is easy for you to graph.

1. Find out period. The period for sin/csc and cos/sec is found by using _________________. The period for tan/cot is found by using ______________

2. Find out L/R shift (based on “h”) 3. Pick scale that works easily with both period and shift. (usually based on the denominator of the shifted

amount; sometimes if the period is also a fraction you have to find the LCD of the two)



“PQ” PROBLEMS: You must complete AT LEAST two graphs of each type (2 sine, 2 cosine, etc). It is suggested you complete all 8 problems for each concept. Print out the graphing chart to fill out for practice. Or, use graph paper and make your own template. Make sure to include all parts of the template if you hand-draw it.

Video and Extra problems We will be working out several of these on video together. (#10,14,18,22,26,30) Any problems we don’t complete on video can be completed for extra practice at home.

Extra Problems # 7,8,11,12,15,16, 19,20,23,24,27,28

are already worked out for you to reference (no video, just work)

Odds answer key

Evens answer key



f(x) = a . sin (b (x – h) ) + k f(x) = a . cos (b (x – h) ) + k

SAMPLE EQUATION

amplitude |a|

period 2π

b 1 mark =

1 mark =

Plot parent

points (5 total)

1. plot beginning and end

2. plot middle

3. plot the midpoints of each

segment

**PLOT PARENT POINTS IN PENCIL

**PLOT SHIFTED POINTS IN

DIFFERENT COLOR

**DECIDE HOW YOU WILL LABEL

YOUR SCALE BASED ON YOUR

SHIFTS AND PERIOD

SINE GRAPHS **starts and ends at 0

COSINE GRAPHS **starts and ends at amplitude

right or left

shift

Based on “h”

up or down

shift

Based on “k”

DOMAIN X-values (interval notation) (-∞,∞) - always (-∞,∞) - always

RANGE y-values (interval notation) Depends on amplitude and shifts

[ , ]

Depends on amplitude and shifts

[ , ]



f(x) = a . csc (b (x – h) ) + k f(x) = a . sec (b (x – h) ) + k

SAMPLE EQUATION

**you will be sketching the corresponding sine

and cosine graph first, so follow the same steps!

amplitude |a|

period 2π

b

1 mark =

1 mark =

Plot parent

points (5 total)

1. plot beginning and end

2. plot middle

3. plot the midpoints of each

segment

**PLOT PARENT POINTS IN

PENCIL

**PLOT SHIFTED POINTS IN

DIFFERENT COLOR

**DECIDE HOW YOU WILL LABEL

YOUR SCALE BASED ON YOUR

SHIFTS AND PERIOD

SINE GRAPHS **starts and ends at 0 – will graph COSECANT

COSINE GRAPHS **starts and ends at amplitude – will graph SECANT

right or left

shift

Based on “h”

up or down shift Based on “k” “k” will always be “0” for us in this class “k” will always be “0” for us in this class

INVERSE

GRAPH

You will have a sketch of the

corresponding sine or cosine

graph in light pencil, and then

you will graph the reciprocal

function in dark pencil based on

the following requirements:

1. vertical asymptotes where the graph crosses the x-axis.

X= _______ + _______n

(1st one) + (½ the period)n

2. Draw graph (looks like a bunch of parabolas) on the

mountains and valleys of the reciprocal graph

1. vertical asymptotes where the graph crosses the x-axis.

X= _______ + _______n

(1st one) + (½ the period)n

2. Draw graph (looks like a bunch of parabolas) on the mountains

and valleys of the reciprocal graph

DOMAIN X-values (interval notation) Depends on asymptotes. Write domain as x ≠ asymptotes

Depends on asymptotes. Write domain as x ≠ asymptotes

RANGE y-values (interval notation) Depends on amplitude and shifts

(-∞, ] U [ , ∞)

Depends on amplitude and shifts

(-∞, ] U [ , ∞)



f(x) = a . tan (b (x – h) ) + k f(x) = a . cot (b (x – h) ) + k

SAMPLE EQUATION

amplitude Tangent and cotangent graphs do

not have amplitudes If “a” is positive, the graph will go uphill

If “a” is positive, the graph will go downhill

period π

b 1 mark =

1 mark =

right or left shift Based on “h” *This shift is taken into account with your

asymptotes (below)

up or down shift Based on “k”

asymptotes b(x-h) = π/2 b(x-h) = -π/2

X= _______ + _______n

(1st one) + (the period)n

b(x-h) = 0 b(x-h) = π

X= _______ + _______n

(1st one) + (the period)n

Plot parent

points (5 total)

1. plot beginning and end asymptotes

2. plot middle point, based on “h” and “k” (tangent starts at (0,0),

while cotangent starts at ( π/2, 0)

3. Draw graph going uphill or downhill, as decided based on “a”

**DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR

SHIFTS AND PERIOD

TANGENT GRAPHS

COTANGENT GRAPHS

DOMAIN X-values (interval notation) Depends on asymptotes. Write domain as x ≠ asymptotes

Depends on asymptotes. Write domain as x ≠ asymptotes

RANGE y-values (interval notation) (-∞,∞) - always (-∞,∞) - always



See kirchmathanalysis.blogspot.com for answer keys and extra videos!

Unit T Practice Test Use the same directions from the PQ problems for each concept to solve these in

order to prepare for the test. Answer key is posted online only at

kirchmathanalysis.blogspot.com

Worked out answer key and video answer key available

Worked out answer key available

unit t student success sheet (sss) t sss - math...video and extra problems we will be working out...

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