Chapter 6.3, Problem 2E

The sign of a trigonometric function of θ depends on the _____ in which the terminal side of the angle θ lies.

In Quadrant II, sin θ is _______ (positive / negative).

In Quadrant III, cos θ is _______ (positive / negative).

In Quadrant IV, sin θ is _______(positive / negative).

To determine

To Evaluate: The dependence of sign of the trigonometric function of $\theta$ and the sign of $\sin \theta$ in Quadrant II, $\cos \theta$ in Quadrant III and $\sin \theta$ in Quadrant IV.

Answer to Problem 2E

The dependence of sign of the trigonometric function of $\theta$ is on the Quadrants and the sign of $\sin \theta$ in Quadrant II is positive, $\cos \theta$ in Quadrant III is negative and $\sin \theta$ in Quadrant IV is negative.

Explanation of Solution

The quadrants tell the sign of trigonometric functions depends on the angle of the trigonometric function.

Every trigonometric function has different sign in the respective four quadrants.

The trigonometric function $\sin \theta$ in Quadrant II is positive because of the angle contains in it.

Thus, the sign in the Quadrant II for $\sin \theta$ is positive.

The trigonometric function $\cos \theta$ in Quadrant III is negative because of the angle contains in it.

Thus, the sign in the Quadrant III for $\cos \theta$ is negative.

The trigonometric function $\sin \theta$ in Quadrant IV is negative because of the angle contains in it.

Thus, the sign of the $\sin \theta$ in Quadrant IV is negative.