Question

10 multiple choice 1 point evaluate the trigonometric function of the given quadrantal angle. sin 20π undefined 1 -1 0 11 multiple choice 1 point evaluate the trigonometric function of the given quadrantal angle. sin (-3π) 0 undefined

Explanation:

Step1: Use the periodicity of sine function

The sine function \(y = \sin(x)\) has a period of \(2\pi\), i.e., \(\sin(x+2k\pi)=\sin(x)\) for any integer \(k\).
For \(\sin(20\pi)\), we can write \(20\pi=2\pi\times10 + 0\). So, \(\sin(20\pi)=\sin(0)\)
Since \(\sin(0) = 0\)

For \(\sin(- 3\pi)\), we know that \(\sin(-3\pi)=\sin(-2\pi-\pi)\)
Using the periodicity \(\sin(x + 2k\pi)=\sin(x)\) with \(k=- 1\), \(\sin(-3\pi)=\sin(-\pi)\)
Also, \(\sin(-\alpha)=-\sin(\alpha)\), so \(\sin(-\pi)=-\sin(\pi)\) and \(\sin(\pi) = 0\), so \(\sin(-3\pi)=0\)

Answer:

For \(\sin(20\pi)\): \(0\)
For \(\sin(-3\pi)\): \(0\)