Question 42 of 50beginner🔧 ApplyVery Short1 mark

Find the values of the trigonometric functions: cosec(-1410°)

Correct Answer

2

Exercise: EXERCISE 3.2 | Q: 7 | (Chapter: 15)
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Explanation

To find cosec(-1410°), we first reduce the angle by adding multiples of 360° since trigonometric functions repeat after an interval of 360°. We calculate -1410° + 4×3604 \times 360° = -1410° + 1440° = 30°. Therefore, cosec(-1410°) = cosec(30°). From the trigonometric values table provided, sin(π/6) = sin(30°) = 1/2. Since cosec x is the reciprocal of sin x, we get cosec(30°) = 1/sin(30°) = 1/(1/2) = 2.

Solution Steps

  1. Step 1: Reduce the angle by adding multiples of 360°: -1410° + 4×3604 \times 360° = -1410° + 1440° = 30°

  2. Step 2: Therefore, cosec(-1410°) = cosec(30°)

  3. Step 3: From the table, sin(30°) = 1/2

  4. Step 4: Since cosec x = 1/sin x, cosec(30°) = 1/(1/2) = 2

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