Question

If cos 0 = - 1/2 and tan 0 > 0, find the quadrant that contains the terminal side of 0, and then find the exact values of the other five trig functions of 0.

Answer 1

The cosine is positive in I and IV
quadrant,negative in II and III quadrant.


The tangent is positive in I and III guadrant,negative in II and IV quadrant.

If cos(theta)<0 cosine is negative
If tan(theta)>0 tangent is positive

Only quadrant where cosine is nagative,and tangent is positive is quadrant III.

sin(theta)= + OR - sqroot[1-cos^2(theta)]

In quadrant III sine is negative so:

sin(theta)= - sqroot[1-cos^2(theta)]

sin(theta)= - sqroot[1-(-1/2)^2]

sin(theta)= - sqroot(1-1/4)

sin(theta)= - sqroot(3/4)

sin(theta)= - sqroot(3) /2

tan(theta)=sin(theta)/cos(theta)=
[-sqroot(3)/2]/(-1/2)= + sqroot(3)=
sqroot(3)

ctg(theta)=1/tan(theta)=1/sqroot(3)

sec(theta)=1/cos(theta)=1/(-1/2)= -2

cosec(theta)=1/sin(theta)=1/[-sqroot(3) /2]= -2/sqroot(3)

Answer 2

determine all trig functions of theta using the given info, state the answers correct to the nearest hundredth.
cos (theta) = -5/13; tan (theta) < 0