3.4 Sum and Difference Formula

Warm-up (IN)1. Find the distance between the points (2,-

3) and (5,1).

2. If and is in quad. II, then

3. a.

b.

Learning Objective: To use the sum and difference formulas to find the sin, cos, and tan of angles not in the unit circle by hand, and to understand and identify which formula is appropriate given a problem.

5

5

4sin -3/5 ._____cos

______3

cos4

sin

______6

sin4

tan

2

4

1/2

NOTES

And the formulas are….

Sinesum

sinsincoscos

sindiff

You need to KNOW these!!

sin

sinsincoscos Cosinesum

sincoscossin

cosdiff cos

sincoscossin

tantan1

tantan

Tangent

sum tan

diff tan

tantan1

tantan

Ex 1 – Find the exact value of

75cos a.

Rewrite using angles you know!

4530cos sinsincoscos

30cos 45cos 30sin 45sin3

2

2

2

1

2

2

2

4

6

4

2

4

26

12cos b.

43cos

sinsincoscos

3cos

4cos

3

sin

4

sin

1

2

2

2

3

2

2

2

4

2

4

6

4

62

12

7cos c.

12

3

12

4cos

43cos

sinsincoscos

3cos

4cos

3

sin

4

sin

1

2

2

2

3

2

2

2

4

2

4

6

4

62

20sin80cos20cos08in d. s

2008in s60ins

2

3

Ex 2 –

:of eexact valu thefind2

3,

5

2in and ,

2,

5

4in If

ss

cos a. 45

35

3

cos b.2

5

1

5

5

cos c. sinsincoscos

3

5

5

5

4

5

2 5

5

25

53

25

58

25

511

in d. s

3

5

5

5

4

5

2 5

5

25

5425

56

25

52

sincoscossin

Ex 3 – Establish

1cotcot

sinsin

cos

sinsincoscos

sinsin

sinsin

coscos

sinsin

sinsin

cot cot 1

HW – pg. 253 #9-13,17,21-24,27-29,31-33

Out – Find

Summary – Today I learned…

Don’t forget about POW!!

cos165