Question

If cos thetha =-0.96 and (sec thetha)(sin thetha)>0 find the value of tan thetha

Answer 1

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)