Question

Which of the following trigonometric expressions has a positive value? Select all that apply.

sec(205°)
tan(205°)
sin(205°)
csc(205°)
cos(205°)
cot(205°)

Answer 1

sec(205°) = → 3rd QUADRANT (NEGATIVE)
tan(205°) = → 3rd QUADRANT (POSITIVE)
sin(205°) = → 3rd QUADRANT (NEGATIVE)
csc(205°) = → 3rd QUADRANT (NEGATIVE)
cos(205°) = → 3rd QUADRANT (NEGATIVE)
cot(205°) = → 3rd QUADRANT (POSITIVE)

Answer 2

tan(205°), cot(205°)

Explanation:

Since, the axes of a two-dimensional Cartesian system divide the plane into four infinite regions, these region are called quadrants,

There are four quadrants,

First quadrant : angles between 0 to 90°,

Second quadrant : angles between 90° to 180°,

Third quadrant : angles between 180° to 270°,

Fourth quadrant : angles between 270° to 360°,

Also all trigonometric functions are positive in first quadrant, in second quadrant only sin and csc are positive, in third quadrant only tan and cot are positive, while, in fourth quadrant only cos and sec are positive.

Since 205° lies on the third quadrant,

Hence, the trigonometric expressions has a positive value are,

tan(205°), cot(205°)