Here, a calculator must be used.

sin(theta) = -0.4545

So, theta = arcsin(-0.4545)

By calculator, theta = -27 degees.

That is if theta were meausured counterclockwise as usual.

The negative then means theta should be measured clockwise. Then theta will fall in the 4th quadrant.

Theta then = 360 -27 = 333 degrees. ....in the usual, counterclockwise, measuring.

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sec(theta) = 2/3

In a calculator, there are no sec or arcsec functions. Only cos or arccos functions.

So convert the sec into cos first so that you can use the calculator.

sec = 1/cos

So, cos = 1/sec

cos(theta) = 1/(2/3) = 3/2 = 1.5

Cannot be.

The maximum value of cos is only 1.0

The question is wrong.