the movement of the progress bar may be uneven because questions can be worth more or less (including zero)…

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. if cos x = √3 / 2, what is the value of cot x? √3 1 2 √3 / 3

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. if cos x = √3 / 2, what is the value of cot x? √3 1 2 √3 / 3

Answer

Explanation:

Step1: Find sin x using identity

We know $\sin^{2}x+\cos^{2}x = 1$. Given $\cos x=\frac{\sqrt{3}}{2}$, then $\sin^{2}x=1 - \cos^{2}x$. Substituting $\cos x$: $\sin^{2}x=1-(\frac{\sqrt{3}}{2})^{2}=1-\frac{3}{4}=\frac{1}{4}$, so $\sin x=\pm\frac{1}{2}$. Since $\cos x=\frac{\sqrt{3}}{2}>0$, in the first - quadrant $\sin x=\frac{1}{2}$ and in the fourth - quadrant $\sin x =-\frac{1}{2}$.

Step2: Calculate cot x

The formula for $\cot x=\frac{\cos x}{\sin x}$. When $\sin x=\frac{1}{2}$ and $\cos x=\frac{\sqrt{3}}{2}$, $\cot x=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}$. When $\sin x =-\frac{1}{2}$ and $\cos x=\frac{\sqrt{3}}{2}$, $\cot x=\frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}$. Assuming we are working in the first - quadrant (since no other information about the domain of $x$ is given), $\cot x=\sqrt{3}$.

Answer:

$\sqrt{3}$