1 Suppose sin x 67 and 32

1) Suppose sin x = -6/7 and 3/2 < x < 2

Find each of the following quantities:

sin (2x)

sec (2x)

cot(x)

2) King Kong stands on the edge of the roof of a 72 foot high building. You poke your head out of a manhole and measure the angles of elevation to the top of King Kong\'s head and to his feet as 69 degrees and 66.1 degrees respectively.

a)How far is your manhole from the building?

b)How tall is King Kong?

Solution

sin x = -6/7 and 3/2 < x < 2

cosx = = -sqrt(6)/7

1) sin2x = 2sinxcosx = 2(-6/7)(-sqrt6/7)

= 12sqrt(6)/49

ii) cos2x = 2cos^2x -1 = 2(-sqrt(13)/7)^2 -1

=2(13/49) -1

= 26/49 -1

= -23/49

secx(2x) = -49/23

iii) cot2x = 1/tan2x = (-23/49) /12sqrt(6)/49

=-23/12sqrt(6)