Answer
sin, csc, cos, sec are negative values and tan and cot are positive values
Work Step by Step
1. Angle in the Quadrant III, between 180 and 270. It will have negative x and y values. r is always positive.
2. Determine the sign:
$\sin\theta=\frac{y}{r}= (-)$
$\cos\theta=\frac{x}{r}= (-)$
$\tan\theta=\frac{y}{x}= (+)$
3. Remember, the reciprocal trig function will have the same sign as the original function
$\csc\theta=(-)$
$\sec\theta=(-)$
$\cot\theta=(+)$
