Evaluating Functions Involving Double Angles In Exercises 21–24, use the given conditions to find the values of sin 2 u , cos 2 u , and tan 2 u using the double-angle formulas. tan u = 3 5 , 0 < u < π 2
Evaluating Functions Involving Double Angles In Exercises 21–24, use the given conditions to find the values of sin 2 u , cos 2 u , and tan 2 u using the double-angle formulas. tan u = 3 5 , 0 < u < π 2
Solution Summary: The author explains that the first category of Trigonometric Identities is functions of multiple angles.
Evaluating Functions Involving Double Angles In Exercises 21–24, use the given conditions to find thevalues of
sin
2
u
,
cos
2
u
, and
tan
2
u
using the double-angle formulas.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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