The angle 60

Question

is shown below in standard position, together with a unit circle.

A circle with a radius of 1 is shown with its center located at the origin on a coordinate grid. The radius forms a terminal side that makes a 60-degree-angle with the positive x-axis. The terminal side intersects the circle at (one half, the square root of 3 over 2).

Use the coordinates of the point of intersection of the terminal side and the circle to compute sec 60
.

Answer 1

To compute \(\sec 60^\circ\), we can use the coordinates of the point of intersection of the terminal side of the \(60^\circ\) angle with the unit circle. The point of intersection is given as \(\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)\).

The secant function is defined as the reciprocal of the cosine function. Therefore:

\[ \sec \theta = \frac{1}{\cos \theta} \]

For \(60^\circ\), we need to find \(\cos 60^\circ\). The cosine of an angle corresponds to the \(x\)-coordinate of the point on the unit circle:

\[ \cos 60^\circ = \frac{1}{2} \]

Now, we can compute \(\sec 60^\circ\):

\[ \sec 60^\circ = \frac{1}{\cos 60^\circ} = \frac{1}{\frac{1}{2}} = 2 \]

Thus, the value of \(\sec 60^\circ\) is:

\[ \sec 60^\circ = 2 \]