State the quadrant and reference angle Then simplify arccsc

State the quadrant and reference angle. Then simplify. arccsc (sec 2 pi/3) arccot (sin 3 pi/2) arccos(sin 0) State the quadrant and reference angle. Then solve for theta [0, 2 pi): cot theta = -15 1/2 sec theta sin theta = sin theta Redo problem 2 for theta R: cot theta = -15 1/2 sec theta sin theta = sin theta

Solution

1)

a)second quadrant

reference angle = -(2_/3) =_/3

arccsc(sec(2_/3))

=arccsc(-2)

=-arccsc(2)

=-_/6

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b)seperating third and fourth quadrant

reference angle =_/2

arccot(sin 3_/2)

=arccot(-1)

=-arccot(1)

=-_/4

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c)

seperating first and fourth quadrant

reference angle =0

arccos(sin0)

=arccos(0)

=_/2