Question 16 of 50beginner🔧 ApplyVery Short1 mark

Find the values of the trigonometric functions: sin(-11π/3)

Correct Answer

3\sqrt{3}/2

Exercise: EXERCISE 3.2 | Q: 9 | (Page 15)
For More Understanding

Explanation

This question tests the understanding of trigonometric functions for negative angles and angles greater than 2π. The solution uses two key properties from the textbook: (1) sin(-x) = -sin x, and (2) values of sin x repeat after an interval of 2π. The student must reduce the angle to a standard position and then evaluate using known values.

Solution Steps

  1. Step 1: Using the property sin(-x) = -sin x, we get sin(-11π/3) = -sin(11π/3).

  2. Step 2: Since values of sin x repeat after an interval of 2π, we reduce 11π/3 by subtracting 2π: 11π/3 - 2π = 11π/3 - 6π/3 = 5π/3.

  3. Step 3: Therefore, sin(11π/3) = sin(5π/3).

  4. Step 4: The angle 5π/3 lies in the fourth quadrant where sin is negative. We have sin(5π/3) = -sin(π/3) = -3\sqrt{3}/2.

  5. Step 5: Hence, sin(-11π/3) = -sin(11π/3) = -(-3\sqrt{3}/2) = 3\sqrt{3}/2.

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