Solve Trigonometric Problems

The angle in the first quadrant makes an angle of \(\frac\) with the positive \(x\)-axis, then so must the angle in the fourth quadrant. We could use \( - \frac\), but again, it’s more common to use positive angles.To get a positive angle all we need to do is use the fact that the angle is \(\frac\) with the positive \(x\)-axis (as noted above) and a positive angle will be \(t = 2\pi - \frac = \frac\). In what follows, it is assumed that you have a good grasp of the trig-ratio values in the first quadrant, how the unit circle works, the relationship between radians and degrees, and what the various trig functions' curves look like, at least on the first period.

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Remember that all this says is that we start at \(\frac\) then rotate around in the counter-clockwise direction (\(n\) is positive) or clockwise direction (\(n\) is negative) for \(n\) complete rotations.

So, the solutions are : \(\frac,\;\frac,\; - \frac,\; - \frac\).

This problem is very similar to the other problems in this section with a very important difference.

), I squared to get this solution, and squaring is an "irreversible" process. If you square something, you can't just square-root to get back to what you'd started with, because the squaring may have changed a sign somewhere.) So, to be sure of my results, I need to check my answers in the , which is the same almost-solution as before.

After doing the necessary check (because of the squaring) and discarding the extraneous solutions, my final answer would have been the same as previously.


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