Find the values of the trigonometric functions of t from the

Find the values of the trigonometric functions of t from the given information.

cos t =

, terminal point of t is in Quadrant III

a) sin t=

b) tan t=

c)sec t=

d)cot t=

e)csc t=

Here we have that as cos x= base/hypotenues

so in such right triangle formed, we have its hypotenues as 5 and base 4 given here, so using pythagorean theorem,

(Hypotenues)^2=height^2+base^2

5^2=4^2+height^2

(height)^2= 25-16=9

or height =3

so sin t= height/hypotenues = -3/5

tan t= height/base = 3/4

cot t=1//tan t = 1/(3/4)= 4/3

sec t = 1/cos t=1/(-4/5)= -5/4

and lastly csc t=1/sin t = 1/(-3/5)= -5//3

Answer