Q.
Consider the statements given below:
I. $\sin \,x$ is positive in first and second quadrants.
II.$ cosec \,x$ is negative in third and fourth quadrants.
III. $\tan \,x$ and $\cot\, x$ are negative in second and fourth quadrants.
IV. $\cos\, x$ and $\sec \,x$ are 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 is correct.
| I | II | III | IV | |
|---|---|---|---|---|
| $\sin x$ | + | + | - | - |
| $\cos x$ | + | - | - | + |
| $\tan x$ | + | - | + | - |
| $cosec x$ | + | + | - | - |
| $\sec x$ | + | - | - | + |
| $\cot x$ | + | - | + | - |