For Exercises 64-68, use the fundamental trigonometric identities as needed. Give that cos x ≈ 0.6691 , Approximate the given function values. Round to 4 decimal places. a. sin x b. sin π 2 − x c. tan x d. cos π 2 − x e. sec x f. cot π 2 − x
For Exercises 64-68, use the fundamental trigonometric identities as needed. Give that cos x ≈ 0.6691 , Approximate the given function values. Round to 4 decimal places. a. sin x b. sin π 2 − x c. tan x d. cos π 2 − x e. sec x f. cot π 2 − x
Solution Summary: The author calculates the value of mathrmsinx, rounded to 4 decimal places, by using fundamental trigonometric identities.
For Exercises 64-68, use the fundamental trigonometric identities as needed.
Give that
cos
x
≈
0.6691
, Approximate the given function values. Round to
4
decimal places.
a.
sin
x
b.
sin
π
2
−
x
c.
tan
x
d.
cos
π
2
−
x
e.
sec
x
f.
cot
π
2
−
x
Equations that give the relation between different trigonometric functions and are true for any value of the variable for the domain. There are six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
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?
University Calculus: Early Transcendentals (4th Edition)
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Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY