use a graphing calculator to graph y₁, y₂, and y₁ + y₂ on the same screen. evaluate each of the three…

use a graphing calculator to graph y₁, y₂, and y₁ + y₂ on the same screen. evaluate each of the three functions at x = $\frac{7pi}{6}$, and verify the following equality. y₁($\frac{7pi}{6}$)+y₂($\frac{7pi}{6}$)=(y₁ + y₂)($\frac{7pi}{6}$) y₁ = sinx, y₂ = sin2x use the graphing functions of your calculator to evaluate y₁ at $\frac{7pi}{6}$. y₁($\frac{7pi}{6}$)=□ (type an integer or decimal rounded to three decimal places as needed.)

use a graphing calculator to graph y₁, y₂, and y₁ + y₂ on the same screen. evaluate each of the three functions at x = $\frac{7pi}{6}$, and verify the following equality. y₁($\frac{7pi}{6}$)+y₂($\frac{7pi}{6}$)=(y₁ + y₂)($\frac{7pi}{6}$) y₁ = sinx, y₂ = sin2x use the graphing functions of your calculator to evaluate y₁ at $\frac{7pi}{6}$. y₁($\frac{7pi}{6}$)=□ (type an integer or decimal rounded to three decimal places as needed.)

Answer

Explanation:

Step1: Recall sine - function value

We know that the sine - function is defined as $y = \sin x$. We need to find $\sin\left(\frac{7\pi}{6}\right)$. The angle $\frac{7\pi}{6}$ is in the third quadrant, and $\frac{7\pi}{6}=\pi+\frac{\pi}{6}$. Using the formula $\sin(A + B)=\sin A\cos B+\cos A\sin B$ with $A=\pi$ and $B = \frac{\pi}{6}$, or the unit - circle definition, we know that $\sin\left(\frac{7\pi}{6}\right)=-\frac{1}{2}=- 0.500$.

Answer:

$-0.500$