Pre Calc

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

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

  • Pre Calc -

    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

  • Pre Calc -

    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

  • Pre Calc -

    any trig function is periodic by 2PI.

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

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