Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg

Last updated at Feb. 13, 2020 by Teachoo

Transcript

Example 24 Solve 2 cos2 x + 3 sin x = 0 2 cos2x + 3 sin x = 0 2 (1 − sin2 x) + 3 sin x = 0 2 – 2 sin2x + 3 sin x = 0 –2sin2x + 3sin x + 2 = 0 Let sin x = a So, our equation becomes sin2 x + cos2 x = 1 cos2 x = 1 – sin2 x –2a2 + 3a + 2 = 0 0 = 2a2 – 3a – 2 2a2 – 3a – 2 = 0 2a2 – 4a + a – 2 = 0 2a (a – 2) + 1 (a – 2) = 0 (2a + 1) (a – 2) = 0 Hence 2a + 1 = 0 2a = –1 a = (−1)/2 a – 2 = 0 a = 2 So, a = (−1)/2 & a = 2 Hence, sin x = (−1 )/2 or sin x = 2 Value of sin is always between −1 and 1 Hence sin x = 2 is not Possible ∴ sin x = (−1)/2 We find its solution Solving sin x = (−𝟏)/𝟐 Let sin x = sin y Given sin x = (−1)/2 From (1) and (2) sin y = (−1)/2 sin y = sin 7𝜋/6 y = 7𝜋/6 Rough We know that sin 30° = 1/2 But we need (−1)/2 So, angle is in 3rd & 4th quadrant θ = 30° 180 + θ = 180 + 30 = 210° = 210 × 𝜋/180 = 7/6 π Rough We know that sin 30° = 1/2 But we need (−1)/2 So, angle is in 3rd & 4th quadrant θ = 30° 180 + θ = 180 + 30 = 210° = 210 × 𝜋/180 = 7/6 π General Solution is x = nπ + (−1)n y where n ∈ Z Putting y = 7𝜋/6 x = nπ + (−1)n 𝟕𝝅/𝟔 Where n ∈ Z

Examples

Example 1

Example 2

Example 3

Example 4

Example 5 Important

Example 6 Important

Example 7 Important

Example 8

Example 9 Important

Example 10

Example 11 Important

Example 12

Example 13

Example 14

Example 15

Example 16 Important

Example 17 Important

Example 18

Example 19 Important

Example 20

Example 21

Example 22 Important

Example 23

Example 24 Important You are here

Example 25 Important

Example 26 Important

Example 27 Important

Example 28 Important

Example 29 Important

Chapter 3 Class 11 Trigonometric Functions

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.