C H A P T E R 5 Analytic Trigonometry
C H A P T E R 5 Analytic Trigonometry
C H A P T E R 5 Analytic Trigonometry
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1. —CONTINUED—<br />
2.<br />
4.<br />
(b)<br />
cos<br />
sin ±1 cos 2 <br />
tan <br />
csc 1<br />
±<br />
sin <br />
sec 1<br />
cos <br />
cot 1<br />
±<br />
tan <br />
2n 1 2n <br />
2 cos 2 3.<br />
cos<br />
cos n cos <br />
sin n sin<br />
2 2<br />
±10 01<br />
0<br />
cos <br />
1 cos 2 <br />
2<br />
n <br />
2n 1<br />
Thus, cos for all integers n.<br />
2 0<br />
pt 1<br />
(a)<br />
The graph of<br />
sin <br />
cos ±1 cos2 <br />
cos <br />
1<br />
1 cos 2 <br />
yields the graph shown in the text and to the right.<br />
—CONTINUED—<br />
4 p 1t 30p 2t p 3t p 5t 30p 6t<br />
p 1t sin524t<br />
p 2t 1<br />
2 sin1048t<br />
p 3t 1<br />
3 sin1572t<br />
p 5t 1<br />
5 sin2620t<br />
p 6t 1<br />
6 sin3144t<br />
p 1 p2 p 3<br />
sin<br />
12n 1<br />
6 <br />
Problem Solving for Chapter 5 525<br />
We also have the following relationships:<br />
sin cos <br />
2<br />
tan <br />
csc <br />
sec 1<br />
cos <br />
cot <br />
cos2 <br />
cos <br />
1<br />
cos2 <br />
cos <br />
cos2 <br />
sin 1<br />
6<br />
sin<br />
2n <br />
sin 1<br />
<br />
6 2<br />
12n <br />
6<br />
12n 1 1<br />
Thus, sin for all integers n.<br />
6 <br />
2<br />
pt 1<br />
1<br />
1<br />
sin524t 15 sin1048t sin1572t sin2620t 5 sin3144<br />
4 t<br />
3 5<br />
1.4<br />
−0.003 0.003<br />
−1.4<br />
p 5 p 6<br />
1.4<br />
−1.4<br />
y<br />
y = p(t)<br />
t<br />
0.006