Chapter 6, Problem 43RE

To determine

To find: The signs of all the six trigonometric function of an angle $\theta$ .

Answer to Problem 43RE

In the first quadrant all the trigonometric function are positive sign.

In the second quadrant all the trigonometric functions are of negative sign except $\sin \theta$ and $\mathrm{cosec}\theta$ .

In the third quadrant all the trigonometric functions are of negative sign except $\tan \theta$ and $\cot \theta$ .

Explanation of Solution

Given information: The terminal side of the angle $\theta$ is in third quadrant.

Calculation:

Since, the terminal side of the angle $\theta$ is in third quadrant.

Therefore $\theta$ may lie in the first, second and third quadrant.

Let’s find the sign of the six trigonometric functions.

In the first quadrant all the trigonometric function are positive sign.

In the second quadrant all the trigonometric functions are of negative sign except $\sin \theta$ and $\mathrm{cosec}\theta$ .

In the third quadrant all the trigonometric functions are of negative sign except $\tan \theta$ and $\cot \theta$ .

Hence, In the first quadrant all the trigonometric function are positive sign.

In the second quadrant all the trigonometric functions are of negative sign except $\sin \theta$ and $\mathrm{cosec}\theta$ .

In the third quadrant all the trigonometric functions are of negative sign except $\tan \theta$ and $\cot \theta$ .