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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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

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk

pi x^2

step-by-step explanation:

pi times x squared