Question

How do you solve the equation `sectheta=2.77` for `0<theta<2pi`?

Answer 1

Solution: For `0 < theta < 360^0 ; Theta ~~ 68.84^0 (2dp), Theta ~~ 291.16^0 (2dp)`

Explanation:

`sec theta =2.77 or 1/cos theta =2.77 or cos theta = 1/2.77 ~~0.3610(4dp) :. theta = cos ^-1(0.3610) ~~68.84^0 (2dp)`

`cos theta` is also positive in 4th quadrant `:. theta=(360-68.84) ~~291.16^0(2dp)`

Solution: For `0 < theta < 360^0 ; Theta ~~ 68.84^0 (2dp), Theta ~~ 291.16^0 (2dp)` [Ans]