use properties of the trigonometric function to find the exact value of each expression. Do no use a calculator.

Question

sec ( - pi/18) * cos (37 pi)/18

I do not see how to do this problem. Every time I do it out I get a reference angle of twenty degrees which isn't on the unit circle. I do it on my calculator and get answer of one. If you could show me how to do this problem that would be great. I think the part I'm getting stuck on is the - pi/8 there must be some other rule that I do not know about when there are negetives

Answer 1

sec(-pi/18)*cos(37PI/18)
Remember that cos(-theta)=cos(theta)
so sec(theta)=sec(-theta)
sec(pi/18)cos(37Pi/18)
sec(2PI +Pi/18)cos(37PI/18)
sec(37pi/18)cos(37PI/18)
1/cos * cos= 1

Answer 2

how did you go from the first line to the next in these lines

sec(2PI +Pi/18)cos(37PI/18)
sec(37pi/18)cos(37PI/18)
1/cos * cos= 1

Answer 3

any trig function is periodic by 2PI.

sin (theta)=sin(theta+2PI)