If tan t=-7/24 and 3*pi/2<t<2 pi, find sin t, cos t, sec t, ccs t, and cot t.

Answer 1

tanx = -7/24 in quadrant IV

cotx = 1/tanx = -24/7 = about -3.43

it's a -7-24-25 right triangle 49+576 = 62

tanx = sinx/cosx = -7/24

sinx = -7/25 = -.28

cscx = 1/sinx = -25/7= 1/.28 = about 3.57

cosx = 24/25= .96

secx = 1/cosx = 25/24 = 1/.96 = about 1.04

or

look at it another way

tanx= -7/25

use an inverse trig function on a scientific calculator

x = about -15.64 degrees or 344.36 degrees

tanx = -7/25 = -.28

tan(-15.64) = -.28

cot(-15.64) = 1/tan(-15.64) = 1/-.28 = -3.57

sin(-15.64) = -.27

cos(-15.64) = .96

sec(-15.64) = 1/cos(-15.64) = 1/.96 = about 1.04

csc(-15.64) = 1/-.27 = about 3.6