Question

Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?

Answer 1

Answer:  Choice B)  $\sqrt{2}$

Work Shown:

$\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}$

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.