Questions: This question: 1 Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator. Submit -π/6 Select the correct choice below and fill in any answer boxes within your choice. A. sin (-π/6)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. cos (-π/6)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. tan (-π/6)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined.

$This question: 1 Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator. Submit -π/6 Select the correct choice below and fill in any answer boxes within your choice. A. sin (-π/6)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. cos (-π/6)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. tan (-π/6)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined.$

Transcript text: This question: 1 Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator. Submit \[ -\frac{\pi}{6} \] Select the correct choice below and fill in any answer boxes within your choice. A. $\sin \left(-\frac{\pi}{6}\right)=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. $\cos \left(-\frac{\pi}{6}\right)=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. $\tan \left(-\frac{\pi}{6}\right)=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function value is undefined.

Solution

Solution Steps

Step 1: Evaluate $\sin\left(-\frac{\pi}{6}\right)$

The sine function is odd, meaning $\sin(-x) = -\sin(x)$. Therefore: \[ \sin\left(-\frac{\pi}{6}\right) = -\sin\left(\frac{\pi}{6}\right). \] We know that $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$, so: \[ \sin\left(-\frac{\pi}{6}\right) = -\frac{1}{2}. \]

Step 2: Evaluate $\cos\left(-\frac{\pi}{6}\right)$

The cosine function is even, meaning $\cos(-x) = \cos(x)$. Therefore: \[ \cos\left(-\frac{\pi}{6}\right) = \cos\left(\frac{\pi}{6}\right). \] We know that $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$, so: \[ \cos\left(-\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}. \]

Step 3: Evaluate $\tan\left(-\frac{\pi}{6}\right)$

The tangent function is odd, meaning $\tan(-x) = -\tan(x)$. Therefore: \[ \tan\left(-\frac{\pi}{6}\right) = -\tan\left(\frac{\pi}{6}\right). \] We know that $\tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}}$, so: \[ \tan\left(-\frac{\pi}{6}\right) = -\frac{1}{\sqrt{3}}. \]