Q.
Consider the statements given below
I. $\sin x$ is positive in first and second quadrants.
II. $\operatorname{cosec} x$ is negative in third and fourth quadrants.
III. $\tan x$ and $\cot x$ are negative in second and fourth quadrant.
IV. $\cos x$ and $\sec x$ is positive in first and fourth quadrants.
Choose the correct option.
Trigonometric Functions
Solution:
The signs of trigonometric functions in different quadrants are shown below.
I
II
III
IV
sin x
+
+
-
-
cos x
+
-
-
+
tan x
+
-
+
-
cosec x
+
+
-
-
sec x
+
-
-
+
cot x
+
-
+
-
According to the above table, option (a) is correct.
| I | II | III | IV | |
|---|---|---|---|---|
| sin x | + | + | - | - |
| cos x | + | - | - | + |
| tan x | + | - | + | - |
| cosec x | + | + | - | - |
| sec x | + | - | - | + |
| cot x | + | - | + | - |