HPC 5.2 Verifying Identities Day 2

HPC 5.2 Verifying Identities

Day 2

Poll

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

$$2\ -\ \csc^2x\ =\ 1-\ \cot^2x$$  

• Right Side

• Left Side

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

"Complicated" is Subjective

Poll

Which substitution would you use to start this problem?

$$2\ -\ \csc^2x\ =\ 1-\ \cot^2x$$  

• $$\csc^2x=\ \cot^2x+1$$  

• $$\cot^2x=\csc^2x-1$$  

• $$\csc^2x=\frac{1}{\sin^2x}$$  

• $$\cot^2x=\ \frac{1}{\tan^2x}$$  

• $$\cot^2x=\frac{\cos^2x}{\sin^2x}$$  

Multiple Choice

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

$$2\ -\ \csc^2x\ =\ 1-\ \cot^2x$$  

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

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

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

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

Poll

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

$$\tan x\ +\ \cot x\ =\ \sec x\csc x$$  

• 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. 

Poll

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

$$\sec x+\tan x\ \ =\ \frac{\cos x}{1-\sin x}$$  

• 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.

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

​(1 + sin x)

​(1 + sin x)

​(. )

Multiple Choice

Which side is the "more complicated"?

$$\tan^3x=\tan x\sec^2x-\tan x$$  

• Right Side

• Left Side

• 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

Draw

Verify:

$$\tan^3x=\tan x\sec^2x-\tan x$$

Poll

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

• Right Side

• Left Side

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

Draw

Verify:

$$\cos^3x\sin^4x\ \ =\ \left(\sin^4x-\sin^6x\right)\cos x$$

Pages 362 - 363

​#6, 14, 17, 31, 34, 41, 47, 51, 55

Homework