Q. 17
Question
Fill in each table entry with the sign of each function.
| sin(x) | cos(x) | tan(x) | sec(x) | cosec(x) | cot(x) | |
| x in Q1 | ||||||
| x in Q2 | ||||||
| x in Q3 | ||||||
| x in Q4 |
Step-by-Step Solution
Verified Answer
| sin(x) | cos(x) | tan(x) | sec(x) | cosec(x) | cot(x) | |
| x in Q1 | + | + | + | + | + | + |
| x in Q2 | + | - | - | - | + | - |
| x in Q3 | - | - | + | - | - | + |
| x in Q4 | - | + | - | + | - | - |
1Step 1. Recollecting information
In first quadrant all the trigonometric functions are positive hence all have sign = +
In second quadrant only sin and cosec functions have positive value
In third quadrant only tan and cot have positive value .
In fourth quadrant only cos and sec are positive
2Step 2. Filling the table
| sin(x) | cos(x) | tan(x) | sec(x) | cosec(x) | cot(x) | |
| x in Q1 | + | + | + | + | + | + |
| x in Q2 | + | - | - | - | + | - |
| x in Q3 | - | - | + | - | - | + |
| x in Q4 | - | + | - | + | - | - |
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