Download MATH 130 Sheet 1

Dakota Wesleyan University
MATH 130 College Algebra and Trigonometry
Concepts addressed:
Define and use the six basic trigonometric relations using degree or radian measure of angles;
know their graphs and be able to identify their period, amplitude, phase displacement or shift,
and asymptotes.
Textbook: Algebra & Trigonometry, 4th Edition, by David Cohen, Brooks/Cole (ISBN 0-31406922-4)
Chapters to review for this concept:
7.1 – Trigonometric Functions of Acute Angles
7.2 – Algebra and the Trigonometric Functions
7.3 – Right-Triangle Applications
7.4 – Trigonometric Functions of Angles
8.1 – Radian Measure
8.4 – Graphs of the Sine and Cosine Functions
8.5 – Graphs of y=A sin(Bx-C) and y=A cos(Bx-C)
8.7 – Graphs of the Tangent and the Reciprocal Functions
Concepts and Terms to review:
Angle: figure formed by two rays with a common endpoint
Vertex: common endpoint of the two rays of an angle
Acute angle: angle θ with degree measure 0° < θ < 90°
Obtuse angle: angle θ with degree measure 90° < θ < 180°
Cosine (cos): adjacent / hypotenuse
Sine (sin): opposite / hypotenuse
Tangent (tan): opposite / adjacent
Secant (sec): 1 / cosine -or- hypotenuse / adjacent
Cosecant (csc): 1 / sine -or- hypotenuse / opposite
Cotangent (cot): 1 / tangent -or- adjacent / opposite
Notational conventions such as: sin2θ = (sinθ)2, 2(sinθ) = 2sinθ, sin(A+B) ≠ sinA + sinB
Basic Identities:
o sin2θ + cos2θ = 1
o sinθ / cosθ = tanθ
o sin(90° - θ) = cosθ -and- cos(90° - θ) = sinθ
o secθ = 1/cosθ, cscθ = 1/sinθ, cotθ = 1/tanθ
Complementary angles: two angles are said to be complementary if their sum is 90°.
Radian measure: the radian measure θ of an angle is the ratio of the arc length s to the
radius r: θ = s / r
180° = π radians:
Development of this review sheet was made possible by funding from the US Department of Education
through South Dakota’s EveryTeacher Teacher Quality Enhancement grant.
o To convert from degrees to radians, multiply by π / 180°
o To convert from radians to degrees, multiply by 180° / π
Periodic function: a function is said to be periodic if it repeats itself at regular intervals.
Period: the length of the portion of the periodic function that repeats itself.
Amplitude: the distance divided by two between the minimum and maximum values of
the function: (M – m)/2
Phase shift: the amount the repeated portion of the function is shifted from the origin.
Shapes and characteristics of the sine, cosine, and tangent functions: y=sin x, y=cos x,
y=tan x
Development of this review sheet was made possible by funding from the US Department of Education
through South Dakota’s EveryTeacher Teacher Quality Enhancement grant.