Trying to learn trig lol

1. Find () given sin()= .8543

Use the sine inverse  [ arcsin] to find { }

arcsin [ .8543 ]  ≈  58.68°  =  {}

2. Find the magnitude of the reference angle for ()=(11pi)/5

Convert radians to degrees   using     180  /pi         ...so we have

(11/5) pi  *  [ 180 / pi ]   =

[11 / 5 ] pi  *  [ 180 / pi ]  =

11 *  180  / 5  =

11 * 36  =

336°

3. Evaluate csc 4.92

csc 4.92   ≈  -1.021945      [ 4.92 is in radians ]

4. Find sec () given that () lies in Quadrant III and tan()= 6

tan  =  y/x      so ..in  Quad III      y = -6   and x  =  - 1

sec  =   x / r       and we can find r  as   

sqrt  [ x^2 + y^2] =  sqrt [ (-1)^2 + (- 6)^2] =

sqrt [ 1 + 36 [  =   sqrt [ 37]  = r

So  sec  =     x / r  =     -1 / sqrt [37]    [   or    -sqrt [ 37] / 37 .... if you prefer ]