7 which of the following is equivalent to sin(6π/13)? a) sin(7π/13) b) sin(19π/13) c) cos(19π/13) d)…

Explanation:

Step1: Recall the property of sine function

The sine - function has the property $\sin(x)=\sin(\pi - x)$. We know that $\sin\left(\frac{6\pi}{13}\right)=\sin\left(\pi-\frac{6\pi}{13}\right)$.

Step2: Calculate $\pi-\frac{6\pi}{13}$

$\pi-\frac{6\pi}{13}=\frac{13\pi - 6\pi}{13}=\frac{7\pi}{13}$. So $\sin\left(\frac{6\pi}{13}\right)=\sin\left(\frac{7\pi}{13}\right)$.

Answer:

A. $\sin\frac{7\pi}{13}$

Explanation for sub - question 8:

Step1: Recall the signs of sine and cosine in different quadrants

In the first quadrant ($0\lt\theta\lt\frac{\pi}{2}$), $\sin\theta>0$ and $\cos\theta>0$. In the second quadrant ($\frac{\pi}{2}\lt\theta\lt\pi$), $\sin\theta>0$ and $\cos\theta<0$. In the third quadrant ($\pi\lt\theta\lt\frac{3\pi}{2}$), $\sin\theta<0$ and $\cos\theta<0$. In the fourth quadrant ($\frac{3\pi}{2}\lt\theta\lt2\pi$), $\sin\theta<0$ and $\cos\theta>0$. Since $\sin\theta < 0$ and $\cos\theta>0$, $\theta$ lies in the fourth quadrant.

Answer:

Fourth quadrant