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 $- 2$ .

$- 2$