Free Printable 5.4 - 1st Assignment - Sum and Difference Identities

1.

The purpose of this Quizizz is to help the student connect their unit circle knowledge to the Sum and Difference Identities.

a)

I remember the Unit Circle.

b)

I don't remember the Unit Circle and I will come back to this assignment today after I practice the Unit Circle today.

2.

a)

I have written all of these identities down in notes. I recognize I will need them later. This can also be found in section 5.4 of my textbook. (hover your mouse over the picture)

b)

I have not written these down, please call my parents.

3.

First, let's remember the Unit Circle. What is the exact value?
cos(60) =

a)

$\frac{\sqrt{2}}{2}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

1

4.

First, let's remember the Unit Circle. What is the exact value?
tan(120) =

a)

$\frac{\sqrt{3}}{2}$

b)

$-\frac{\sqrt{3}}{2}$

c)

$-\frac{1}{2}$

d)

1

e)

$-\sqrt{3}$

5.

First, let's remember the Unit Circle. What is the exact value?
sin( $-\frac{\pi}{2}$ ) =

a)

$-\frac{\sqrt{2}}{2}$

b)

0

c)

$-\frac{1}{2}$

d)

-1

6.

First, let's remember the Unit Circle. What is the exact value?
tan( $-\frac{7\pi}{4}$ ) =

a)

$-\frac{\sqrt{2}}{2}$

b)

0

c)

$-\frac{1}{2}$

d)

-1

e)

1

7.

Now let's investigate the sum of two angles using the identities you wrote down earlier.

sin(60) should equal sin(90 - 30)

Which equation should we use to prove this?

a)

sin(90)cos(30) + cos(90)sin(30)

b)

sin(90)cos(30) - cos(90)sin(30)

c)

cos(90)cos(30) - sin(90)sin(30)

d)

cos(90)cos(30) + sin(90)sin(30)

8.

Now let's investigate the sum of two angles using the identities you wrote down earlier.

sin(60) should equal sin(90-30)

Which of the following show this?

a)

$\left(\sin90\right)\left(\cos30\right)+\left(\cos90\right)\left(\sin30\right)$

b)

$\frac{\tan90-\tan\ \left(\frac{\pi}{6}\right)}{1+\tan\left(\frac{\pi}{2}\right)\tan30}$

c)

$\left(\cos90\right)\left(\frac{\sqrt{3}}{2}\right)-\left(1\right)\left(\frac{1}{2}\right)$

d)

$\left(1\right)\left(\frac{\sqrt{3}}{2}\right)-\left(\cos\ \frac{\pi}{2}\right)\left(\frac{1}{2}\right)$

9.

The reason Sum and Difference formulas are useful is that they allow us to find the exact value of angles that are not generally memorized on the unit circle. For instance:

sin(75) = sin(45 + 30)

a)

$\left(\sin45\right)\left(\frac{1}{2}\right)-\left(\frac{\sqrt{2}}{2}\right)\left(\sin30\right)$

b)

$\left(\sin45\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{2}\right)$

c)

$\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)+\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)$

d)

$\left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)$

e)

$\left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{3}}{2}\right)-\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)$

10.

$\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)+\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)$

Now let's practice simplifying this expression

a)

$-\frac{\sqrt{2}}{2}$

b)

$\frac{\sqrt{2}}{2}$

c)

$-\sqrt{2}$

d)

$\sqrt{2}$

e)

$\frac{\sqrt{2}}{4}$

11.

Select all of the following that are true.

a)

I can retake this quizizz as many times as I need until I understand.

b)

I can log into Ms. Crutcher's office hours by clicking the link in Google Classroom under "Classwork"

c)

Ms. Crutcher's office hours are Tuesday and Thursday from 9:30am - 11am AND 2:00pm - 3:30pm

d)

Next, I complete my Khan Academy assignment.

e)

I can find all of my assignments listed by dates in Google Classroom under "Classwork".

5.4 - 1st Assignment - Sum and Difference Identities

Total questions: 11

Worksheet time: 39mins

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