Chapter 9.7, Problem 34E

a.

To determine

To find: Sign of $\sin \theta ,cos\theta ,\text{ and tan}\theta$ .

Answer to Problem 34E

  $\sin \theta =+ve,cos\theta =-ve,\text{ and tan}\theta =-ve$

Explanation of Solution

Given information:

A unit circle is shown below.

  

Calculation:

  

In above unit circle angle $\theta$ lies in second quadrant. In second quadrant sine of an angle is positive while cosine and tangent of an angle is negative.

Therefore, $\sin \theta =+ve,cos\theta =-ve,\text{ and tan}\theta =-ve$ .

b.

To determine

To find: The quadrant in which terminal side of angle $-\theta$ lies.

Answer to Problem 34E

Third quadrant.

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

  

In above unit circle terminal side of angle $-\theta$ lies in third quadrant.

c.

To determine

To find: Sign of $\sin \left(-\theta \right),cos\left(-\theta \right),\text{ and tan}\left(-\theta \right)$ .

Answer to Problem 34E

  $\sin \left(-\theta \right)=-ve,cos\left(-\theta \right)=-ve,\text{ and tan}\left(-\theta \right)=+ve$

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

  

In above unit circle terminal side of angle $-\theta$ lies in third quadrant. In third quadrant sine and cosine of angle is negative while tangent of an angle is positive.

Therefore, $\sin \left(-\theta \right)=-ve,cos\left(-\theta \right)=-ve,\text{ and tan}\left(-\theta \right)=+ve$ .