Suppose cos θ = √2/2 for some θ between 0° and 90°. Find the exact value of sec θ and identify the value of θ.

Question

Suppose cos θ =   for some θ between 0° and 90°. Find the exact value of sec θ and identify the value of θ.

a. 

b. 

c. 

d. 

Answer 1

cosθ=√2/2, secθ=1/cosθ=2/√2=√2 and θ=45°. (In a square the diagonal bisects the 90° angle of each vertex and the length of the diagonal is √2 times the length of the side of the square, hence cos45=1/√2 which rationalises to √2/2.) Answer option a.