Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 123: 11

(a) $1$ (b) $0$ (c) undefined

You are given that $s=\frac{\pi}{2}$. (a) $\sin$(s) = $\sin(\frac{\pi}{2})$ An angle of $\frac{\pi}{2}$ intersects the unit circle at the point $(0,1)$, and since $sine$ gives the y-coordinate, the value of $\sin(\frac{\pi}{2})$ is 1. (b) $\cos(s) = \cos(\frac{\pi}{2})$ An angle of $\frac{\pi}{2}$ intersects the unit circle at the point $(0,1)$, and since $cosine$ gives the x-coordinate, the value of $\cos(\frac{\pi}{2})$ is 0. (c) $\tan(s) = \tan(\frac{\pi}{2})$ An angle of $\frac{\pi}{2}$ intersects the unit circle at the point $(0,1)$, and since $\tan$ gives $\frac{y}{x}$, the value of $\tan(\frac{\pi}{2})$ is undefined, because $\frac{1}{0}$ gives a math error.