Question 12 of 50intermediate🔧 ApplyShort Answer2 marks

Find the values of other five trigonometric functions: tan x = -5/12, x lies in second quadrant.

Correct Answer

sin x = 5/13, cos x = -12/13, cot x = -12/5, sec x = -13/12, cosec x = 13/5

Exercise: EXERCISE 3.2 | Q: 5 | (Page 15)
For More Understanding

Explanation

This question from Exercise 3.2 tests understanding of trigonometric identities and sign conventions in different quadrants. In the second quadrant, sin x and cosec x are positive, while cos x, sec x, tan x, and cot x are negative. The solution follows the same method as Example 7 in the textbook, using fundamental identities to find all other trigonometric functions.

Solution Steps

  1. Step 1: Find cot x = 1/tan x = -12/5

  2. Step 2: Use sec²x = 1 + tan²x = 1 + 25/144 = 169/144, so sec x = ±13/12

  3. Step 3: Since x lies in second quadrant, sec x is negative, hence sec x = -13/12

  4. Step 4: Find cos x = 1/sec x = -12/13

  5. Step 5: Use sin²x = 1 - cos²x = 1 - 144/169 = 25/169, so sin x = 5/13 (positive in second quadrant)

  6. Step 6: Find cosec x = 1/sin x = 13/5

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