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Ex 2.1, 5 - Find principal value of cos-1 (-1/2) - Inverse

Ex 2.1, 5 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Ex 2.1, 5 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

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Ex 2.1, 5 Find the principal value of cos−1 (−1/2) Let y = cos−1 ((−1)/2) cos y = (−1)/2 cos y = cos (𝟐𝝅/𝟑) Since Range of cos−1 is [0 , 𝜋] Hence, the principal value is 𝟐𝝅/𝟑 Rough We know that cos 60° = 1/2 θ = 60° = 60° × 𝜋/180 = 𝜋/3 Since (−1)/2 is negative Principal value is 𝝅 – θ i.e. π −𝜋/3 = 𝟐𝝅/𝟑 Ex 2.1, 5 (Method 1) Find the principal value of cos−1 (−1/2) Let y = cos−1 ((−1)/2) y = 𝜋 − cos−1 (1/2) y = 𝜋 − 𝝅/𝟑 y = 𝟐𝝅/𝟑 Since Range of cos−1 is [0, 𝜋] Hence, the principal value is 𝟐𝝅/𝟑 We know that cos−1 (−x) = 𝜋 − cos−1 x Since cos 𝜋/3 = 1/2 𝜋/3 = cos−1 (1/2) Ex 2.1, 5 (Method 2) Find the principal value of cos−1 (−1/2) Let y = cos−1 ((−1)/2) cos y = (−1)/2 cos y = cos (𝟐𝝅/𝟑) Since Range of cos−1 is [0, 𝜋] Hence, the principal value is 𝟐𝝅/𝟑 Rough We know that cos 60° = 1/2 θ = 60° = 60° × 𝜋/180 = 𝜋/3 Since (−1)/2 is negative Principal value is 𝝅 – θ i.e. π −𝜋/3 = 𝟐𝝅/𝟑

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.