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 ]
