STUDY GUIDE, CHAPTER 10
10.1 #1 Sketch angles in standard position and find coterminal angles.
10.1 #2 Convert angles from degrees to radians and vice versa.
10.1A Use the formula s = rq to find the distance traveled by the tip of the minute hand or second hand of a clock in a given length of time (Lesson 10.1A, example 1 and problems 3 or 4).
10.2 #1 Reproduce from memory the values of the sinq. cosq and tanq for 0, 30, 45, 60 and 90 degrees (0, p/6, p/4, p/3 and p/2 radians).
10.2 #2 Reproduce from memory the definitions of the sinq. cosq and tanq in terms of x, y and r and in terms of the adjacent side, opposite side and hypotenuse.
10.2 #3 Know the domain and range of the sine, cosine, and tangent functions.
10.2 #4 Find the exact values of sinq. cosq and tanq at any multiple of the special angles
Ex: tan (−11π/3), sin (5π/6), cos (7π/3)
10.3 #1 Reproduce from memory the trig identities in this lesson and those discussed earlier:
Ratio identity for the tangent (tanq = sinq/cosq)
Pythagorean identity for sinq. cosq: sin2θ + cos2θ = 1
Negative angle identities: sin(-q) = -sin(q), etc.
Periodicity identities: sin t = sin(t ± 2π); cos t = cos(t ± 2π), tan t = tan(t ± π)
10.3 #2 Be able to use the fundamental identities to simplify trig expressions.
10.3 #3 Factor trig
expressions: example: 2 sin2
x + 3 sin x + 1
10.4 #1 Know the basic graphs of the sine, cosine, and tangent functions
10.4 #2 Graph the sine, cosine, and tangent functions with transformations
Ex: y = 3 sin (t − 2); y = − cos t + 1
10.5 #1 Graph functions of the form y=A×sin(bt+c) and y=A×cos(bt+c).
10.5 #2 Find the amplitude, period, and phase shift of y=A×sin(bt+c) and y=A×cos(bt+c).
10.5A Express sinusoidal graphs in the form Asin(bt+c)
10.6 #1 Reproduce from memory the definitions of all 6 trig functions in terms of x, y and r and in terms of the adjacent side, opposite side and hypotenuse.
10.6 #2 Reproduce from memory the fundamental identities for all 6 functions, i.e.:
Reciprocal identities (csc q = 1/sinq, sec θ = 1/cos θ, cot θ = 1/tan θ)
Ratio identities for the tangent and cotangent (tanq = sinq/cosq, cotq = cosq/sinq)
Additional Pythagorean identities involving tangent and secant; cotangent and cosecant
10.6 #3 Convert all 6 trig functions to angles (in degrees or radians) and vice versa, in any quadrant (use reference angles).
10.6 #4 Graph the remaining trig functions (csc t, sec t, cot t)
From the graphs, identify the domains, ranges, periods
Return to: Merced College; Don Power Updated 11/01/05 by Don Power