6. (3 pts) Find the exact value of cos 2 arcsin cos2: Solution (0, 0.5, 1) Let x=arcsin Then sinx = 5/13 and -/2≤x≤/2 by definition of the arcsine function. Using a double-angle identity for cosine, we simplify the given expression as follows to find its exact value: (0, 1) for a double-angle identity cos(2 arcsin()) = cos (2x) = 1-2sin²x (0, 0.5, 1) 2(25) 169-50 119 = = 1- = 13 169 169 169 Alternative Solutions: One may also use the following two alternative forms of the double-angle identity for cosine, and construct the right-triangle shown on the right in conjunction with the Pythagorean Theorem to determine the needed quantities: cos(2x)=cosx-si x-sin²x or cos(2x)=200sx-1 sin x 5/13 13 5 √13-5-12
6. (3 pts) Find the exact value of cos 2 arcsin cos2: Solution (0, 0.5, 1) Let x=arcsin Then sinx = 5/13 and -/2≤x≤/2 by definition of the arcsine function. Using a double-angle identity for cosine, we simplify the given expression as follows to find its exact value: (0, 1) for a double-angle identity cos(2 arcsin()) = cos (2x) = 1-2sin²x (0, 0.5, 1) 2(25) 169-50 119 = = 1- = 13 169 169 169 Alternative Solutions: One may also use the following two alternative forms of the double-angle identity for cosine, and construct the right-triangle shown on the right in conjunction with the Pythagorean Theorem to determine the needed quantities: cos(2x)=cosx-si x-sin²x or cos(2x)=200sx-1 sin x 5/13 13 5 √13-5-12
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 10E
Related questions
Question
Can you show the steps of how to get this answer, and explain all the steps.
Transcribed Image Text:6. (3 pts) Find the exact value of cos 2 arcsin
cos2:
Solution
(0, 0.5, 1)
Let x=arcsin
Then sinx = 5/13 and -/2≤x≤/2 by definition of the arcsine function.
Using a double-angle identity for cosine, we simplify the given expression as follows to find its exact
value:
(0, 1) for a double-angle identity
cos(2 arcsin())
=
cos (2x)
=
1-2sin²x
(0, 0.5, 1)
2(25)
169-50
119
=
= 1-
=
13
169
169
169
Alternative Solutions: One may also use the following
two alternative forms of the double-angle identity for
cosine, and construct the right-triangle shown on the right
in conjunction with the Pythagorean Theorem to
determine the needed quantities:
cos(2x)=cosx-si
x-sin²x or cos(2x)=200sx-1
sin x 5/13
13
5
√13-5-12
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