In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
angle θ: < 2π
positive
Step 02:
We must use the Cartesian plane and the reference angles to fill the table.
Table
θ in QI θ in QII θ in QIII θ in QIV
reference angle θ π - θ θ - π 2π - θ
sin-1 (sin θ) θ
cos-1 (cos θ) θ
θ in QI :
θ
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = angle
= θ
θ in QII :
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = 180 - angle
= π - angle
= π - θ
θ in QIII :
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = angle - 180
= θ - π
θ in QIV :
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = 360 - angle
= 2π - θ
That is the solution.
