Question

Find each value of θ in degrees (0° < θ < 90°) and radians (0 < θ < π/2) without using a calculator.

a) csc θ = square root of 2

b) sin θ = (square root of 2)/(2)

Answer 1

if you can't use a calculator then you need to memorize (or use) the unit circle
http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcircle.htm

you also need some identities to solve a) like, \(csc~\theta=\dfrac{1}{sin\theta}\)