Ch 9

Question 1

Name the three Pythagorean Identities.

Answer 1

relates sin and cos: (sin θ)^2 + (cos θ)^2 = 1

relates tan and sec: 1 + (tan θ)^2 = (sec θ)^2

relates cot and csc: 1 + (cot θ)^2 = (csc θ)^2

Question 2

What are Cofunction Identities? And name the pairings.

Answer 2

sin(𝜋/2 - θ) = cos θ, vice versa
csc(𝜋/2 - θ) = sec θ, vice versa
tan(𝜋/2 - θ) = cot θ, vice versa

Question 3

Negative Angle Identities: When θ is negative, all trig functions must keep the negative sign EXCEPT for ___

Answer 3

cos/sec because they are even functions

cos(-θ) = cos θ, sec(-θ) = sec θ

Question 4

sin (a + b)

Answer 4

sin acos b + cos asin b

Question 5

cos (a + b)

Answer 5

cos acos b - sin asin b

Question 6

tan (a + b)

Answer 6

tan a + tan b
———————
1 - tan a*tan b

Question 7

sin (a - b)

Answer 7

sin acos b - cos asin b

Question 8

cos (a - b)

Answer 8

cos acos b + sin asin b

Question 9

tan (a - b)

Answer 9

tan a - tan b
———————
1 + tan a*tan b

Question 10

Area of a Triangle Formula when given an angle and its adjacent sides (SAS)

Answer 10

Area = (1/2)(side)(side)*(sin of angle)

Question 11

Law of Sines

Answer 11

The ratios of the sin of each angle to its opposite side are equal. Example:

sinA/a = sinB/b = sinC/c

a/sinA = b/sinB = c/sinC