Let , where is measured in…

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Let

f(\theta)=\tan \theta+\sec \theta

, where

\theta

is measured in radians. (i) Determine all values of

\theta

in the interval

[0,\,2\pi]

for which

f(\theta)

is undefined. (ii) How many points of discontinuity does

f

have in the closed interval

[0,\,8\pi]

? Show your reasoning. (iii) On each open sub-interval of continuity of

f

[0,\,2\pi]

, does

f

attain a maximum or minimum value? Give a brief justification.