Question 9 of 50intermediate🔧 ApplyShort Answer2 marks

Find the values of other five trigonometric functions: sin x = 3/5, x lies in second quadrant.

Correct Answer

Given: sin x = 3/5, x lies in second quadrant.

Using the identity sin²x + cos²x = 1, we get: cos²x = 1 - sin²x = 1 - (3/5)² = 1 - 9/25 = 16/25 Therefore, cos x = ±4/5

Since x lies in the second quadrant, cos x is negative. Therefore, cos x = -4/5.

Now, sec x = 1/cos x = -5/4 and csc x = 1/sin x = 5/3.

Also, tan x = sin x/cos x = (3/5)/(-4/5) = -3/4 and cot x = 1/tan x = -4/3.

Exercise: EXERCISE 3.2 | Q: 2 | (Page 15)
For More Understanding

Explanation

This question follows the same pattern as Example 7 in the textbook. The key steps are: (1) Use the Pythagorean identity sin²x + cos²x = 1 to find cos x, (2) Apply the quadrant rule to determine the sign (in second quadrant, sin is positive, cos is negative), and (3) Use reciprocal and quotient identities to find the remaining functions. The textbook context confirms that in the second quadrant, sec x is negative and sin x is positive.

Solution Steps

  1. Step 1: Use sin²x + cos²x = 1 to find cos²x = 1 - 9/25 = 16/25

  2. Step 2: Therefore cos x = ±4/5

  3. Step 3: Apply quadrant rule - in second quadrant, cos x is negative, so cos x = -4/5

  4. Step 4: Find sec x = 1/cos x = -5/4

  5. Step 5: Find csc x = 1/sin x = 5/3

  6. Step 6: Find tan x = sin x/cos x = -3/4

  7. Step 7: Find cot x = 1/tan x = -4/3

PreviousNext