Question

Determine the signs of the six trigonometric functions of an angle $\theta$whose terminal side is in quadrant III.

Short answer

The trigonometric functions are sine, cosine, cosecant, secant

Step-by-step solution

Given information

Given terminal side is in quadrant III

Checking the trigonometric rules

Locating the angle in quadrant III, since it below the $x$-axis and and left side of the $y$ axis. Then, sine and cosine functions are negative. The reciprocal of sine function is cosecant and the reciprocal of cosine function is secant, so they are also negative. Thus, cosecant and secant functions are negative. Tangent and cotangent functions are both ratio of sine and cosine which had negative values making them positive. Hence, tangent and cotangent functions are positive.