Question 15 of 50beginner🔧 ApplyVery Short1 mark

Find the values of the trigonometric functions: tan 19π/3

Correct Answer

3\sqrt{3}

Exercise: EXERCISE 3.2 | Q: 8 | (Page 15)
For More Understanding

Explanation

This question is from Exercise 3.2, Question 8. The solution uses the principle stated in the context that 'values of tan x will repeat after an interval of π'. The angle 19π/3 is reduced by subtracting multiples of π until we reach a standard angle π/3, whose tangent value is 3\sqrt{3}.

Solution Steps

  1. Step 1: We know that values of tan x repeat after an interval of π.

  2. Step 2: Reduce 19π/3 by multiples of π: 19π/3 = 18π/3 + π/3 = 6π + π/3

  3. Step 3: Since tan has period π, tan(19π/3) = tan(6π + π/3) = tan(π/3)

  4. Step 4: Therefore, tan(19π/3) = 3\sqrt{3}

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