ap calculus ab
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04/20/23 Perkins
AP Calculus AB
Day 1Trig (Appendix Section 3)
Review of Trigonometry
0 30 45 60 90
Sin
Cos
Tan
2
2
2
2
1
2
1
2
3
2
3
2
1
33
0
0
0
1
1
1
6
4
3
2
Give in simplified radical form.
1. sin135 2. cos225
3. cot300 4. sec 150
1
2or
2
2
QII QIII
QIV QIII
45
1
12 or
1 2
22
451
12
60
2
1
3or
1 3
33 or
2 2 3
33
30
21
3
Identities you should know:
tan
cot
csc
sec
sin
cos
1 cos
tan sin
1
sin1
cos
2 2sin cos
2sec
21 cot
1
21 tan
2csc
Even / Odd Properties
sin
cos
tan
sec
csc
cot
sin
cos
tan
sec
csc
cot
Compare the values of the trig function in QI and QIV.
Solve on the interval .
5. cos2 2 3sin
0,2
2 2cos sin 2 3sin 2 21 sin sin 2 3sin
21 2sin 2 3sin 20 2sin 3sin 1
0 2sin 1 sin 1
0 2sin 1 0 sin 1 1
sin2
1 sin
5,
6 6
2
Trig Graphs
2 3
2 2
1
1
2 3
2 2
1
1
cosy x
siny x
cosy A B x C D
siny A B x C D
Amplitude
Period
Phase shift
Vertical shift
2
B
Height of each ‘wave’.
Length of one ‘wave’.
Re-center the graph at x = C.
Re-center the graph at y = D.
A
C
D
2 3
2 2
1
1
2 3
2 2
1
1
cscy x secy x
secy A B x C D cscy A B x C D Create these graphs by making the sine or cosine graphs first
and then taking the reciprocal of each y-value.
Amplitude
PeriodPhase shiftVertical shift
1
sin x 1
cos x
Only applies to sine and cosine.
All are the same as sine and cosine
Amplitude
Doesn’t really apply (not a wave)
Gives a point the graph passes through
Period
Repeats twice as fast as sin, cos, sec, csc
Phase shift, Vertical shift
4
2 3
4
1
1
tany x
A
B
Same as sin, cos, sec, csc
coty x
4
2 3
4
1
1
1
tan x
Graph one period, beginning at zero.
4
2 3
4
2
2
24 2cos 2y x Amplitude
Period
Phase shift
Vertical shift
22
2
42s4 2coy x
40x
4x
Re-center graph at
4 up4
4
6
1
Perkins
AP Calculus AB
Day 1Trig (Appendix Section 3)
Review of Trigonometry
0 30 45 60 90
Sin
Cos
Tan
Give in simplified radical form.
1. sin135 2. cos225
3. cot300 4. sec 150
Identities you should know:
tan
cot
csc
sec
sin
cos
1 cos
tan sin
1
sin1
cos
2 2sin cos
2sec
21 cot
1
21 tan
2csc
Even / Odd Properties
sin
cos
tan
sec
csc
cot
sin
cos
tan
sec
csc
cot
Compare the values of the trig function in QI and QIV.
Solve on the interval .
5. cos2 2 3sin
0,2
Trig Graphs
cosy x
siny x
cosy A B x C D
siny A B x C D
Amplitude
Period
Phase shift
Vertical shift
cscy x secy x
secy A B x C D cscy A B x C D Create these graphs by making the sine or cosine graphs first
and then inverting individual points.
Amplitude
PeriodPhase shiftVertical shift
Amplitude
Period
Phase shift, Vertical shift
tany x coty x
Graph one period, beginning at zero. 24 2cos 2y x Amplitude
Period
Phase shift
Vertical shift
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