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.
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.
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.
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]