MATH SOLVE

4 months ago

Q:
# Evaluate the expression Arcsec(sqrt 2). Do not use your calculator to answer this question. Do not express answer in decimals.

Accepted Solution

A:

pi/4 radians

You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.

sqrt(2) = 1/x

x*sqrt(2) = 1

x = 1/sqrt(2)

Let's multiply both numerator and denominator by sqrt(2), so

x = sqrt(2)/2

And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:

45 * (2*pi)/360 = 90*pi/360 = pi/4

So your answer is pi/4 radians.

You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.

sqrt(2) = 1/x

x*sqrt(2) = 1

x = 1/sqrt(2)

Let's multiply both numerator and denominator by sqrt(2), so

x = sqrt(2)/2

And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:

45 * (2*pi)/360 = 90*pi/360 = pi/4

So your answer is pi/4 radians.