Trigonometry Examples

$\sec (\arccos (\frac{1}{2}))$

Step 1

Draw a triangle in the plane with vertices $(\frac{1}{2}, \sqrt{1^{2} - {(\frac{1}{2})}^{2}})$ , $(\frac{1}{2}, 0)$ , and the origin. Then $\arccos (\frac{1}{2})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\frac{1}{2}, \sqrt{1^{2} - {(\frac{1}{2})}^{2}})$ . Therefore, $\sec (\arccos (\frac{1}{2}))$ is $2$ .

$2$