pre calculus! in need of help asap! thanks!

Question

I understand how to do these type of questions in sin, cos, and tan but don't know how to do these..

 

Without the use of the calculator determine the exact value of each trigonometric ratio.

 

a) sec Pi/3

 

b) cot 3/4 Pi

 

c) csc (-Pi)

 

Thanks!

Answer 1

a) sec(∏/3)=sec(180/3)=sec(60)

sec=1/cos

sec(60)=1/cos(60)

cos(60)=1/2 on the unit circle

1/(1/2)=2 (answer)

 

b)cot(3/4*∏)=cot(135)

cot=cos/sin

cot(135)=cos(135)/sin(135)

cos(135)=-√2/2 on the unit circle

sin(135)=√2/2 on the unit circle

(-√2/2)/(√2/2)=-1 (answer)

 

csc(-180)=1/sin(-180)

sin(180)=0

1/0 is undefined (answer)