Aaron4thw
06.11.2021 •
Mathematics
Find sin(2x), cos(2x), and tan(2x) from the given information.
sec(x) = 8, x in Quadrant IV
sin(2x) = 3
х
cos(2x) =
tan(2x) =
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Ответ:
If x terminates in the fourth quadrant, then we know that sin(x) < 0 and cos(x) > 0. Given that sec(x) = 8, we immediately have
cos(x) = 1/sec(x) = 1/8
Recall the Pythagorean identity,
cos²(x) + sin²(x) = 1
Then it follows that
sin(x) = -√(1 - cos²(x)) = -3√7/8
Now recall the double angle identities,
sin(2x) = 2 sin(x) cos(x)
cos(2x) = cos²(x) - sin²(x)
Then
sin(2x) = 2 (-3√7/8) (1/8) = -6√7/64 = -3√7/32
cos(2x) = (1/8)² - (-3√7/8)² = -62/64 = -31/32
By definition of tangent,
tan(x) = sin(x)/cos(x)
Then
tan(2x) = sin(2x)/cos(2x) = (=3√7/32) / (-31/32) = 3√7/31
Ответ:
[(5*9)/3]-(1+9)=5
first you would to five times nine and one plus nine:
(45)/3-(10)
then divide 45 by three.
()
doing so would give you five as an answer.