Review for Test #3 MATH 1113 (Chapter 5, 6.1)
5.1: Angles and Their Measure 13, 15, 17, 19, 21, 25, 27, 31, 33, 37, 39, 43, 45, 49, 51, 55, 57, 59, 63, 65, 67, 69, 73, 75, 77, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 107
· Be able to state and apply the definition of radian measure
· Be able to convert from radians to degrees and degrees to radians
· Be able to convert from degrees to degrees/minutes/seconds (DMS) and DMS to degrees
· Be able to apply, define, and provide a measurement of an angle in standard position
· Be able to find arc length subtended by a given angle
· Be able to calculate the arc length, perimeter and area of a sector of a circle.
· Be able to calculate linear and angular speeds of points on a circle/disk/wheel
5.2: Trigonometric Functions 15, 17, 21, 23, 25, 27, 29, 31, 35, 37, 41, 43, 45, 47, 51, 55, 59, 61, 65, 69, 77, 85, 89, 91, 93
· Be able to state and apply the definition of the six trigonometric functions
· Know the trigonometric function value and the radian measure of the good angles
o (30 degrees, 45 degrees and 60 degrees)
o as well as any angle which has a good angle as its reference angle.
· Know all the trigonometric function values and the radian measures of the quadrantal angles
o (0 degrees, 90 degrees, 180 degrees, and 270 degrees)
· Know/apply definitions of trigonometric functions in terms of circles other than the unit circle.
5.3: Properties of Trig. Functions 13, 19, 29, 31, 33, 37, 41, 45, 47, 53, 55, 57, 61, 69, 77, 83, 85, 87, 89, 91, 93, 94 (Answer:-1) , 115
· Given the sine or cosine (but not both) of an angle and quadrant for its terminal side, be able to find the exact values other five trigonometric functions of the angle.
· Given a trigonometric function value of a number and some information to determine quadrant, be able to find the exact values other five.
· Be able to state and apply the fundamental identities
o the basic trigonometric identities (write in terms of sine and cosine)
o pythagorean identities
o periodic identities as well as the even/odd identities
· For functions y = cosx and y = sinx, know the domain, range, period and amplitude, even/odd
· For functions y = tanx, y = cotx, y = secx, y = cscx,
o know the domain, range, period and the equations of the vertical asymptotes, even/odd
5.4: Graphs of Sine and Cosine 15, 17, 19, 21, 37, 39, 43, 45, 65, 69, 73, 77, 79, 81, 83
· For functions y = Acos(Bx), y = Asin(Bx), be able to
o graph the function over any subset of its domain
o sketch a graph labeling all maxima, minima, and horizontal intercepts (if any) and vertical intercept (if any) with their EXACT coordinates over any subset of the domain
o find an equation for a given graph
5.5: Graphs of Tangent, Secant, Cosecant, Cotangent Functions 9, 11, 13, 17, 19, 21, 23, 27, 29, 33, 35, 39, 41
· For functions y = Acot(Bx+C), y = Atan(Bx+C), y = Acsc(Bx+C), and y = Asec(Bx+C), be able to
o find the domain and range
o sketch a graph labeling all of the horizontal intercepts (if any) and vertical intercept (if any) with their EXACT coordinates over any subset of the domain
o label all vertical asymptotes with their exact equations over any subset of the domain
5.6: Phase Shift, Sinusoidal Curve Fitting 5, 7, 9, 11, 13, 23
· For functions y = Acos(Bx+C), y = Asin(Bx+C) be able to find the domain and range as well as sketch a graph labeling all maxima, minima, and horizontal intercepts (if any) and vertical intercept (if any) with their EXACT coordinates over any subset of the domain
· Approximation of a curve of the form y = Asin(Bx+C)+D to sinusoidal data and Sinusoidal Regression
6.1: Inverse Sine, Cosine and Tangent Functions 15, 21, 41, 43, 45, 47, 49, 51, 53, 55
· Graphs of inverse sine, inverse cosine and inverse tangent functions and finding exact values of inverse sine, inverse cosine and inverse tangent functions and compositions with standard trig. functions
Radian Measure
Place the vertex of an angle at the center of a circle with radius r. Let s be the arc length of the circle subtended by the angle. The radian measure q of the angle is given by provided that r and s are measured in the same linear units.
Circular Trigonometric Functions
Let q be a measure of an angle in standard position. Let P with coordinates (x,y) be the point of intersection of the terminal side of the angle with the unit circle x2 + y2 = 1. Then, define the (circular) trigonometric functions of q by
Periodic Functions and Period
A function f is periodic if and only if there is a positive real number p such that, for every real number q, if q is in the domain of f then (1) so is q + p and (2) f(q + p) = f(q). If there is a smallest such real number p, then this smallest value is called the period of function f.
Amplitude
Let f be a periodic function and let m and M denote, respectively, the minimum and maximum values of f. If both m and M exist, the amplitude of f is the number (M – m)/2