What is the circumference of latitude 0$^o$S if R is the radius of the earth?

1. Analyze the Question

The question asks for the circumference of a specific latitude on the Earth's surface. You are given the latitude as $0^\circ$S and the radius of the Earth as $R$.

2. Explain the Concept

• Latitude $0^\circ$: This is the Equator. The Equator is a "Great Circle," meaning it is the largest circle that can be drawn on the Earth's surface.
• General Formula: The radius ($r$) of a circle of latitude at an angle $\theta$ is given by $r = R \cos \theta$, where $R$ is the radius of the Earth.
• Circumference Formula: The circumference of any circle is $2\pi r$. Substituting the radius of the latitude, the formula becomes: $$\text{Circumference} = 2\pi R \cos \theta$$

3. Show the Solution

• Step 1: Identify the latitude angle ($\theta$). Here, $\theta = 0^\circ$.
• Step 2: Recall the trigonometric value for $\cos 0^\circ$. We know that $\cos 0^\circ = 1$.
• Step 3: Apply the formula for the circumference of a latitude: $$\text{Circumference} = 2\pi R \cos \theta$$ $$\text{Circumference} = 2\pi R \cos 0^\circ$$ $$\text{Circumference} = 2\pi R (1)$$ $$\text{Circumference} = 2\pi R$$

4. Identify the Answer

Looking at the options provided: A. $\cos \theta$ B. $2\pi R \cos \theta$ C. $R \sin \theta$ D. $2\pi r \sin \theta$

While the specific value for $0^\circ$ is $2\pi R$, the general formula for the circumference of any latitude $\theta$ is represented by option B. In JAMB questions of this type, they often ask for the general formula expression. Therefore, option B is the correct representation of the circumference of a latitude.

5. Exam Tip

Always remember the "Cos" rule for latitudes: "Latitude uses Cosine, Longitude uses Sine." If you are asked for the radius of a parallel of latitude, always multiply the Earth's radius ($R$) by the cosine of the latitude angle.