…csc theta = 5/3 to determine the position of a boating accident. If theta is on the interval (pi/2, pi), find the exact value of tan 2theta + cos theta/2.

from geometry csc theta=1/sin theta

hence 1/sin theta=5/3

this implies that sin theta=3/5 (inverse of 5/3)

and theta = Arcsin(3/5)

= 36.86 degrees

tan 2theta + cos theta/2 = tan (2*36.86) + cos(36.86/2)

=tan 73.72 + cos 18.43

= 3.42+0.95

=4.37

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