If sin ? = -4/5 and tan ? = 4/3, find sec ?.

Question

Choices are ;

 

-5/3

 

5/3

 

3/5

 

-3/5

Answer 1

Again all the trigonometry exposed.

sec x=1/cos x

sin/cos=4/3

cos x=sin x/(4/3)=(-4/5)/(4/3)=-3/5

Sec x = -5/3.

The angle is in the third quadrant.

Answer 2

Recall than secx=1/cosx

 

Now since tanx=sinx/cosx, sinx/tanx=cosx, and hence tanx/sinx=secx