trig expression for every angle coterminal to s

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How do you write an expression to represent every angle coterminal to s?

Given: s in a unit circle with point (-1/2 , -sqrt(3)/2)

I got that it is quadrant 3, and the trig functions are those of angle 60°. I also got that the reference angle is pi/3. But I don't know how to write the expression.
 
You don't need the trig-function values, nor the first-quadrant "reference" angle. You just need to find the given angle, and then an expression for every angle that "ends" at the same spot.

With the point being (-1/2, -sqrt(3)/2) -- that is, with each of x and y being negative -- this is, as you point out, in the third quadrant. Drawing the terminal side through this point, you can quickly confirm that the measure of angle s, assuming you're measuring from the x-axis (that is, from 0°), is 180° + 60° = 240°.

The "next" angle that ends there is "once around" from there, or 240° + 360°. (Don't simplify.) The "next" one is 240° + 360° + 360° = 240° + 2(360°). The one "before" is 240° - 360°. (Again, don't simplify.) The one "before" that is 240° - 360° - 360° = 240° - 2(360°).

Keep going until you see the pattern, and can figure out where the variable (the counter, for "times around") should go.

Eliz.
 
Since it's on a unit circle, isn't it measured in radians rather than degrees?
 
You can measure it either way. You referred to "60°", so I stayed with "degrees". If you want to use radians, just convert.

Eliz.
 
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