approximate the real number value for y=sec inverse (4.7963825)

Question

approximate the real number value for y=sec inverse (4.7963825)

Answer 1

y = sec^-1(4.7963825) [take the secant of both sides of the equation to get:

sec(y) = sec(sec^-1(4.7963825)

sec(y) = 4.7963825 [divide both sides by sec(y) and both sides by 4.7963825 to get:

1/4.7963825 = 1/sec(y) [use the reciprocal identity cos(y) = 1/sec(y) to get:

1/4.7963825 = cos(y)

0.2084904613 = cos(y) [take the cos inverse of both sides to get:

cos^-1(0.2084904613) = cos^-1(cos(y))

cos^-1(0.2084904613) = y

y = 77.96609592° or y = 1.360765079 radians

However, there can be other values that also work for this as well (reference the unit circle). -77.96609592° would also work or other angle measures that are multiples of 360°