Questions: 13) sec -3 π 14) cot 13π/6 15) tan 7π/2 16) cot -π

Transcript text: 13) $\sec -3 \pi$ 14) $\cot \frac{13 \pi}{6}$ 15) $\tan \frac{7 \pi}{2}$ 16) $\cot -\pi$

Solution

Solution Steps

Step 1: Evaluating sec(-3π)

The secant function has a period of 2π, so sec(-3π) = sec(-3π + 2π + 2π) = sec(π). Since sec(x) = 1/cos(x), we have sec(π) = 1/cos(π) = 1/(-1) = -1.

Step 2: Evaluating cot(13π/6)

The cotangent function has a period of π, so cot(13π/6) = cot(13π/6 - 2π) = cot(π/6). Since cot(x) = cos(x)/sin(x), we have cot(π/6) = cos(π/6)/sin(π/6) = (√3/2)/(1/2) = √3.

Step 3: Evaluating tan(7π/2)

The tangent function has a period of π, so tan(7π/2) = tan(7π/2 - 3π) = tan(π/2). Since tan(x) = sin(x)/cos(x), we have tan(π/2) = sin(π/2)/cos(π/2) = 1/0, which is undefined.

Final Answer:

-1
√3
Undefined

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