cos(theta)=-0.96 <0
=>
theta is either in the 2nd or third quadrant.
cos(theta)=-0.96
=>
sec(theta)=1/cos(theta)=-1/0.96 <0
Given sec(theta)(sin(theta)>0
=> cos(theta)sin(theta)>0
=> cos(theta) and sin(theta) have the same sign,
=> sin(theta)<0
=>
theta is in the third quadrant. => tan(theta)>0
Given cos(theta)=-0.96
=>
|sin(theta)|=sqrt(1-(-0.96)^2)=sqrt(0.0784)=0.28
=> sin(theta)=-0.28
Finally,
tan(theta)=sin(theta)/cos(theta)=-0.28/-0.96
=7/24
=0.29167 (to the fifth decimal place)
