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HPC 5.2 Verifying Identities Day 2

HPC 5.2 Verifying Identities Day 2

Assessment

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Easy

•
CCSS
HSF.TF.B.7

Standards-aligned

Created by

Shane Devlin

Used 16+ times

FREE Resource

6 Slides • 9 Questions

1

HPC 5.2 Verifying Identities

Day 2

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2

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3

Poll

Which side of this equation is the most "complicated"?

2 − csc⁡2x = 1− cot⁡2x2\ -\ \csc^2x\ =\ 1-\ \cot^2x  

Right Side

Left Side

All of Life is complicated right now. There's really no way to tell.

4

"Complicated" is Subjective

5

Poll

Which substitution would you use to start this problem?

2 − csc⁡2x = 1− cot⁡2x2\ -\ \csc^2x\ =\ 1-\ \cot^2x  

csc⁡2x= cot⁡2x+1\csc^2x=\ \cot^2x+1  

cot⁡2x=csc⁡2x−1\cot^2x=\csc^2x-1  

csc⁡2x=1sin⁡2x\csc^2x=\frac{1}{\sin^2x}  

cot⁡2x= 1tan⁡2x\cot^2x=\ \frac{1}{\tan^2x}  

cot⁡2x=cos⁡2xsin⁡2x\cot^2x=\frac{\cos^2x}{\sin^2x}  

6

Multiple Choice

Which of the following approaches/advice do you think is most important to avoid mistakes on this problem?

2 − csc⁡2x = 1− cot⁡2x2\ -\ \csc^2x\ =\ 1-\ \cot^2x  

1

When substituting, use parenthesis and remember to distribute the negative sign.

2

Change everything to sine and cosine, it will be easier.

3

Rewrite everything using definitions in terms of x, y and r to make it more clear.

4

Mistake? A horse walks into a bar and the bartender says, "Why such a long face?"

7

Poll

Which side of this equation is the most "complicated"?

tan⁡x + cot⁡x = sec⁡xcsc⁡x\tan x\ +\ \cot x\ =\ \sec x\csc x  

Right Side

Left Side

Complicated.  I'll tell you what's complicated.  My alphabet soup was missing the letter L.  Of course, it was from Christmas, so that was appropriate. 

8

9

Poll

Which side of this equation is the most "complicated"?

sec⁡x+tan⁡x  = cos⁡x1−sin⁡x\sec x+\tan x\ \ =\ \frac{\cos x}{1-\sin x}  

Right Side

Left Side

Complicated.  I'll tell you what's complicated. When I woke up this morning all my lamps were gone. 

Strangely though, I was delighted.

10

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​Hint: start by multiplying the right side by (1 + sin x) on top and bottom.

​(1 + sin x)

​(1 + sin x)

​(. )

11

Multiple Choice

Which side is the "more complicated"?

tan⁡3x=tan⁡xsec⁡2x−tan⁡x\tan^3x=\tan x\sec^2x-\tan x  

1

Right Side

2

Left Side

3

Complicated? I'll tell you what's complicated, waiting for the new marvel movie about the constipated superhero. Waiting. . . Waiting. . . Waiting. Sadly, it still hasn't come out yet

12

Draw

Verify:

tan⁡3x=tan⁡xsec⁡2x−tan⁡x\tan^3x=\tan x\sec^2x-\tan x

13

Poll

Which side of this equation is the most "complicated"? cos⁡3xsin⁡4x  = (sin⁡4x−sin⁡6x)cos⁡x\cos^3x\sin^4x\ \ =\ \left(\sin^4x-\sin^6x\right)\cos x  

Right Side

Left Side

Complicated.? I used to wonder why frisbees looked bigger the closer they got. . . Then it hit me!"

14

Draw

Verify:

cos⁡3xsin⁡4x  = (sin⁡4x−sin⁡6x)cos⁡x\cos^3x\sin^4x\ \ =\ \left(\sin^4x-\sin^6x\right)\cos x

15

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Pages 362 - 363

​#6, 14, 17, 31, 34, 41, 47, 51, 55

Homework

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HPC 5.2 Verifying Identities

Day 2

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