Question

Question #0cb79

Answer 1

Use either the trig definition of the secant function, or the identity `sec^2(x) = 1 + tan^2(x)`. See explanation for answer.

Explanation:

Recall that secant is simply `1/(cosx)`, and that `sec^2(x) = (sec x)^2`.

Since `sin (pi/4) = cos (pi/4) = 1/sqrt2, sec (pi/4) = 1/(1/sqrt2) = sqrt2, and sec^2(pi/4) = sqrt 2 ^2 = 2`

Alternately, recall that `sec^2(x) = 1 + tan^2(x)`. Since we know the sin and cosine are equal, the tangent must be 1, meaning we have `1 + tan^2(pi/4) = 1 + 1^2 = 1+1 = 2`

Either way, the answer is `y(pi/4) = 2`