Semester 1 Final

Question 1

Law of Sines

Answer 1

SinA/a = SinB/b = SinC/c

Question 2

Law of Cosines

Answer 2

a^2 = b^2 + c^2 -2bc • cos(A)

Question 3

Reciprocal Identities

Answer 3

Sin(x) = 1/Csc(x)
Cos(x) = 1/Sec(x)
Tan(x) = 1/Cot(x)

Question 4

Quotient Identities

Answer 4

Tan(x) = Sin(x)/Cos(x)
Cot(x) = Cos(x)/Sin(x)

Question 5

Pythagorean Identities

Answer 5

sin^2x + cos^2x = 1
1 + tan^2x = sec^2x
1+ cot^2x = csc^2x

Question 6

Cofunction Identities

Answer 6

Sin(pi/2-theta) = Cos(theta)
Tan(pi/2-theta) = Cot(theta)
Sec(pi/2-theta) = Csc(theta)

Question 7

Even-Odd Identities

Answer 7

Sin(-x) = -Sin(x)
Tan(-x) = -Tan(x)
Cos(-x) = Cos(x)

Question 8

Sum or Difference Identities

Answer 8

Sin(x+-y) = Sin(x)Cos(y) +- Cos(x)Sin(y)
Cos(x+-y) = Cos(x)Cos(y) -+ Sin(x)Sin(y)
Tan(x+-y) = Tan(x) +- tan(y) / 1 -+ Tan(x)Tan(y)

Question 9

Sin Graph

Answer 9

x = -2pi through 2pi
y = -1 through 1
increasing through origin and decreasing to 3pi/2

Question 10

Cos Graph

Answer 10

x = -2pi through 2pi
y = -1 through 1
Decreasing from (0,1) to pi then increasing pi to 2pi

Question 11

Arc length

Answer 11

Multiply degree by pi/180 then by radius