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What does 1 divided by sin x look like?

Updated: 4/28/2022
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9y ago

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1/sin(x) is also known as cosec(x).

It looks a bit like a U, starting at "infinity" when x = 0, bottoming out at 1 when x = pi/2 radians and then returning to "infinity" at x = pi. Next, it is an upside down U, below the axis and peaking at -1: between x = pi and 2*pi. These U shapes alternate.

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1 (sec x)(sin x /tan x = (1/cos x)(sin x)/tan x = (sin x/cos x)/tan x) = tan x/tan x = 1


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First we look at the double-angle identity of cos2x. We know that: cos2x = cos^2x - sin^2x cos2x = [1-sin^2x] - sin^2x.............. (From sin^2x + cos^2x = 1, cos^2x = 1 - sin^2x) Therefore: cos2x = 1 - 2sin^2x 2sin^2x = 1 - cos2x sin^2x = 1/2(1-cos2x) sin^2x = 1/2 - cos2x/2 And intergrating, we get: x/2 - sin2x/4 + c...................(Integral of cos2x = 1/2sin2x; and c is a constant)


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(tan x + cot x)/sec x . csc x The key to solve this question is to turn tan x, cot x, sec x, csc x into the simpler form. Remember that tan x = sin x / cos x, cot x = 1/tan x, sec x = 1/cos x, csc x = 1/sin x The solution is: [(sin x / cos x)+(cos x / sin x)] / (1/cos x . 1/sin x) [(sin x . sin x + cos x . cos x) / (sin x . cos x)] (1/sin x cos x) [(sin x . sin x + cos x . cos x) / (sin x . cos x)] (sin x . cos x) then sin x. sin x + cos x . cos x sin2x+cos2x =1 The answer is 1.


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2 sin2(x) + sin(x) - 1 = 0(2 sin + 1) (sin - 1) = 0Either 2 sin(x) + 1 = 02sin(x) = -1sin(x) = -0.5x = 210°, 330°or sin(x) - 1 = 0sin(x) = 1x = 90°


What is the simplest form for tanx divided by secx?

Need the fundamental identities here. tan(X) = sin(X)/cos(X) sec(X) = 1/cos(X) so tan(X)/sec(X) same as, sin(X)/cos(X) * cos(X)/1 cancel the cos(X) = sin(X) ---------------simplest form

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