Topics for Exam 2
Math 131 Spring 2011
The second exam will cover everything we have talked about since the exam 1. Specifically, sections 3.3 3.5, 3.7, 3.8, and 4.1- 4.3. Again, the quizzes and homework are good problems to make sure you can do.
Also, with each homework assignment there are a bunch of suggested exercises. You should make sure you
can do all of these.
Here is a sort of checklist for you to make sure you know everything that might be on the exam. You
should be able to do each of the following tasks.
2 Establish trigonometric identities.
2 Use the sum and difference formulas to find the exact value of a trig function. (Ex: sin(15◦ ))
2 Use the double and half angle formulas to find the exact value of a trig function.
2 Establish identities using the sum/difference/double/half angle formulas.
2 Solve simple trig equations.
2 Solve trig equations using trig identities and factoring
2 Solve right triangles
2 Solve triangles using the Law of Sines
2 Solve triangles using the Law of Cosines
2 Solve word problems involving triangles.
Attached you will find a copy of the formula sheet we will provide you on the exam. In addition, you
should know the following formulas:
tan θ =
csc θ =
1
sin θ
sin2 θ + cos2 θ = 1
sin θ =
Opp
Hyp
sin θ
cos θ
sec θ =
cot θ =
1
cos θ
tan2 θ + 1 = sec2 θ
cos θ =
Adj
Hyp
Happy Studying!
cos θ
sin θ
cot θ =
1
tan θ
cot2 θ + 1 = csc2 θ
tan θ =
Opp
Adj
Sum and Difference Formulas
cos (α + β) = cos α cos β − sin α sin β,
cos (α − β) = cos α cos β + sin α sin β
sin (α + β) = sin α cos β + cos α sin β,
sin (α − β) = sin α cos β − cos α sin β
tan (α + β) =
tan α + tan β
,
1 − tan α tan β
Double Angle Formulas:
sin (2θ) = 2 sin θ cos θ
cos (2θ) = cos2 θ − sin2 θ
cos (2θ) = 1 − 2 sin2 θ
cos (2θ) = 2 cos2 θ − 1
tan (2θ) =
2 tan θ
1 − tan2 θ
Half-angle Formulas:
q
α
sin α2 = ± 1−cos
2
q
α
cos α2 = ± 1+cos
2
q
α
tan α2 = ± 1−cos
1+cos α
Half-angle Formulas for tan α2
tan α2 =
1−cos α
sin α
=
sin α
1+cos α
Let 4ABC be a triangle with side lengths a, b, c.
The Law of Sines
sin A
sin B
sin C
=
=
a
b
c
The Law of Cosines
a2 = b2 + c2 − 2bc cos A
b2 = a2 + c2 − 2ac cos B
c2 = a2 + b2 − 2ab cos C
tan (α − β) =
tan α − tan β
1 + tan α tan β