Question

1. sec 900°

Explanation:

Step1: Use the periodicity of the secant function

The secant function \(y = \sec x=\frac{1}{\cos x}\), and \(\cos(x + 360^{\circ}n)=\cos x\), \(n\in\mathbb{Z}\).
For \(x = 900^{\circ}\), we can write \(900^{\circ}=2\times360^{\circ}+180^{\circ}\).
So \(\sec900^{\circ}=\sec(2\times360^{\circ} + 180^{\circ})\).
Since \(\sec(x + 360^{\circ}n)=\sec x\) (\(n\in\mathbb{Z}\)), then \(\sec900^{\circ}=\sec180^{\circ}\).

Step2: Calculate the value of \(\sec180^{\circ}\)

We know that \(\sec x=\frac{1}{\cos x}\), and \(\cos180^{\circ}=- 1\).
So \(\sec180^{\circ}=\frac{1}{\cos180^{\circ}}=\frac{1}{-1}=-1\).

Answer:

\(-1\)