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.
trig - Anonymous, Saturday, May 14, 2011 at 12:09pm
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
[-sqroot(3)/2]/(-1/2)= + sqroot(3)=
cosec(theta)=1/sin(theta)=1/[-sqroot(3) /2]= -2/sqroot(3)
trig - anna, Tuesday, October 4, 2011 at 10:23pm
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