Chapter 13, Trigonometric Ratios and Functions - 13.3 Evaluate Trigonometric Functions of Any Angle - 13.3 Exercises - Problem Solving - Page 872: 40

$60^{\circ}$

Let the $a$ be the radius of the circle of the latitude. Here, $\cos \theta =\dfrac{a}{r} \implies a=r \cos \theta$ Thus, we have $ 2 \pi r =\pi r \implies r=2a$ Now, $2 r \cos \theta=r$ This gives: $\cos \theta=\dfrac{1}{2}$ Thus, $\theta=60^{\circ}$