Chapter 4.3, Problem 13E

Solution

(a)

To find: The sign $(+\text{or}-)$ of $\sin t$ for the values of $t$ in the interval $\left(0,\frac{\pi }{2}\right)$ .

  $+$

Given information:

The functions $\sin t$

Calculation:

All trigonometric functions are positive in the first quadrant where the angle lies between 0 and $\frac{\pi }{2}$ .

Then, in the interval $\left(0,\frac{\pi }{2}\right)$ ,

  $\sin t$ is positive (+)

(b)

To find: The sign $(+\text{or}-)$ of $\cos t$ for the values of $t$ in the interval $\left(0,\frac{\pi }{2}\right)$ .

  $+$

Given information:

The functions $\cos t$

Calculation:

All trigonometric functions are positive in the first quadrant where the angle lies between 0 and $\frac{\pi }{2}$ .

Then, in the interval $\left(0,\frac{\pi }{2}\right)$ ,

  $\cos t$ is positive (+)

(c)

To find: The sign $(+\text{or}-)$ of $\tan t$ for the values of $t$ in the interval $\left(0,\frac{\pi }{2}\right)$ .

  $+$

Given information:

The functions $\tan t$ .

Calculation:

All trigonometric functions are positive in the first quadrant where the angle lies between 0 and $\frac{\pi }{2}$ .

Then, in the interval $\left(0,\frac{\pi }{2}\right)$ ,

  $\tan t$ is positive (+)