Hello all,

I just need to confirm some answers to some questions I have attempted, unfortunately i do not have the solutions to them:

1.) evalute arctan (2 sin (-pi/3))

my solution: first i evaluated 2 sin (-pi/3)

since sin (-pi/3) = - root (3) / 2 and since it is multiplied by 2, we now have arctan (-root 3)

which again from the triangle i found to equal -pi/3.

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2.) arccos( cosec (pi/2)).

cosec (pi/2) = 1 / sin (pi/2) = 1

so we have: arccos (1) and cos x = 1

so x: 2n * pi where n is any integer.

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3.) cos (arcsin (-root 3 / 2) + arccos (root 2 / 2))

the solution is very long-winded so i will cut it short.

by using the cos (x-y) formula after evaluating the terms in the brackets i got root 3 + 1 / 2 * (root 2) as the final answers.

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4.) Find the implied domain and range of h(x) = log (sec (x))

range: [0, inf)

domain: all real values excluding integer multiples of the region [pi/2, 3pi/2] where the range is below [1, inf]

Regards.