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.
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
The maximum value of cos is only 1.0
The question is wrong.