Pre calculus

1. Reference angle for -280 degrees?

I do not understand why you add 360????

2. Theta=? If reference angle =60 and theta terminates in quadrant 3.

What does terminate mean?
Please show work and explain why.
My priority is to understand the concept ...

3. Exact value for sec theta if theta=-150 degrees
Please explain and show work

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  1. First step, add/subtract multiples of 180° until you have an angle between -180° and 180°

    If θ is in QI, you're done.

    If θ is in QIII, reflect through the origin. That is, add 180°. Done.

    If θ is in QIV, y<0, so reflect through the x-axis. That is, add 180°.

    Then, if θ is in QII, reflect it in the y-axis so x>0. That is, subtract θ from 180°.

    SO, for -280°,
    add 180: -100°
    Now θ is in QIII, so 1dd 180: 80°

    The rules get messy, and there are lots of ways to express things. Study your text, google reference angle on the web, until you find a method that makes sense. You want to end up in QI for the reference angle.

    #2 Reference angle is 60, but θ is in QII, where x<0 and y<0. So rotate θ through 180°, so it winds up as 240°.

    #3
    reference angle for -150° is 30°.
    So, since -150° is in QIII, x<0 and y<0.
    secθ = r/x = 1/(-√3/2) = -2/√3

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