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substitute t = 1, t=2 and t =3 in the equation and see if its value exceeds 38

Is it 4t=2.6179 + 2pi(n)?

why? your system is defined by the equation you are given. what is all this talk about quadrants?

No sir

cosine of both positive and negative numbers always exists.

Right so in which quadrants is inverse sin positive?

2nd quadrant i believe

or rather, in the 1st and 4th quadrants

I have calculated the cosines in radians, I am not sure if you have to convert them to degrees.

That is what I got, also. Yes - I calculate only in radians. Thank you for your time/help!

But how do you know to solve for t=.2773?

Holy crap I'm so confused.
Obviously not, because I solved for P(1.7010), P(2.2253)...etc