find the exact values below. if applicable, click on \undefined.\ cos(19π/6)= tan(-90°)=

Explanation:

Step1: Rewrite $\frac{19\pi}{6}$

Express $\frac{19\pi}{6}$ as $2\pi+\frac{7\pi}{6}$. Since $\cos(x + 2\pi)=\cos(x)$, then $\cos(\frac{19\pi}{6})=\cos(2\pi+\frac{7\pi}{6})=\cos(\frac{7\pi}{6})$.

Step2: Find $\cos(\frac{7\pi}{6})$

The angle $\frac{7\pi}{6}$ is in the third - quadrant. We know that $\cos(\frac{7\pi}{6})=\cos(\pi+\frac{\pi}{6})$. Using the formula $\cos(A + B)=\cos A\cos B-\sin A\sin B$ with $A=\pi$ and $B = \frac{\pi}{6}$, we have $\cos(\pi+\frac{\pi}{6})=-\cos(\frac{\pi}{6})=-\frac{\sqrt{3}}{2}$.

Step3: Analyze $\tan(-90^{\circ})$

The tangent function is defined as $\tan\theta=\frac{\sin\theta}{\cos\theta}$. For $\theta=- 90^{\circ}$, $\cos(-90^{\circ}) = 0$ and $\sin(-90^{\circ})=-1$. Since division by zero is undefined, $\tan(-90^{\circ})$ is undefined.

Answer:

$\cos(\frac{19\pi}{6})=-\frac{\sqrt{3}}{2}$, $\tan(-90^{\circ})$ is undefined.