Question #0cb79

1 Answer
Nov 9, 2017

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#