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```Math 115
Notes for Exam 1
Spring 2017
The first exam will be Wednesday, February 22nd and will cover the topics we have studied
in Chapters 1 and 2. I recommend studying assigned homework problems as well as examples
discussed in class. For extra practice, there is a review section at the end of each chapter in
the text as well as many homework problems that weren’t assigned that you can try. All the
previously assigned homework is listed on ginasmathclasses.com.
• General: you need to have the following memorized:
For an angle with vertex at the origin, initial side along the positive x-axis and given
a point (x, y) on the terminal side:
x
r
y
sin θ =
r
y
tan θ =
x
cos θ =
r
x
r
csc θ =
y
x
cot θ =
y
sec θ =
Given a right triangle:
sin θ =
opp
,
hyp
cos θ =
,
hyp
tan θ =
opp
Ratio Identities:
tan θ =
sin θ
cos θ
cot θ =
Pythagorean Identities:
cos θ
sin θ
cos2 θ + sin2 θ = 1
Reciprocal Identities:
1
csc θ =
sin θ
1
tan θ =
cot θ
1 + tan2 θ = sec2 θ
1
sec θ =
cos θ
1 + cot2 θ = csc2 θ
Co-Function Theorem: If α + β = 90◦ :
sin α = cos β
sec α = csc β
tan α = cot β
Co-function Identities:
sin θ = cos(90◦ − θ)
sec θ = csc(90◦ − θ)
tan θ = cot(90◦ − θ)
• Section by section:
Section 1.1 (a) Know the relationship between the sides of 60◦ − 30◦ − 90◦ triangles and 45◦ −
45◦ − 90◦
(b) Know the definitions from this section: Initial side, terminal side, line, ray,
angle, obtuse, acute, supplementary, complementary.
(c) Be able to find the exact measure of angles that are supplementary or complementary. Also, find the angles in a triangle algebraically.
Section 1.2 (a) Know the definition of similar triangles.
(b) Be able to use similar triangle ratios to find unknown lengths.
Section 1.3 (a) Know the definition of all the trigonometric functions as they relate to right
triangles.
(b) Given a triangle, be able to find the value of all six trigonometric functions.
Section 1.4 (a) Be able to derive the exact values of sin θ, cos θ and tan θ for θ = 30◦ , 60◦ and
45◦ using the known relationships of the triangles from Section 1.1.
(b) Be able to convert from degrees-minutes-seconds to decimal and back.
(c) Know how to use your calculator to evaluate trigonometric values.
Section 1.5 (a) Be able to use the inverse trigonometric functions to find angles.
(b) Given 2 sides of a right triangle or 1 side and 1 angle be able to find the remaining
sides and angles.
Section 2.1 (a) Be able to sketch an angle in standard position.
Section 2.2 (a) Given a point on the terminal side of an angle in the plane, be able to find the
values of all 6 trigonometric functions of the angle.
(b) Be able to find the values of the trigonometric functions of the angle any line
through the origin makes with the positive x-axis.
Section 2.3 (a) Given the value of one trigonometric function and the quadrant the terminal
side lies in, be able to find all other trig values.
(b) Be able to use reference angles to find exact values of angles in each quadrant.
(c) Be able to find all angles that have a particular trigonometric value on the unit
circle.
Section 2.4 (a) Know the ratio, reciprocal and Pythagorean identities.
(b) Know how to use the above identities and a given value to find the remaining
values of the trigonometric functions.