Question

Find these quantities:
i. Find all angles in the unit circle with secx=2.1754 . Give your answers in
radians to 4 decimal places.
ii. Find sec(arcsin(2x))

Answer 1

secx = 2.1754
x = 0.4776

SInce secx is positive in QI and QIV, the other angle is 2π-0.4776

arcsin(2x) makes no sense, since x is an angle. That's if we are still referring to the first question.

Now, in general, if sinθ = 2x, then
cosθ = √(1-sin^2θ) = √(1-4x^2)
So, secθ = 1/√(1-4x^2)