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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 3.2, 1 Find the values of other five trigonometric functions if cos⁡𝑥 = – 1/2 , x lies in third quadrant. Since x is in 3rd Quadrant sin and cos will be negative But, tan will be positive Given cos x = (−1)/2 We know that sin2 x + cos2 x = 1 sin2 x + ((−1)/2)^2 = 1 sin2 x + 𝟏/𝟒 = 1 sin2 x = 1 – 1/4 sin2 x = (4 − 1)/4 sin2x = 𝟑/𝟒 sin x = ±√(3/4) sin x = ± √𝟑/𝟐 Since x is in 3rd Quadrant And, sin x is negative in 3rd Quadrant ∴ sin x = −√𝟑/𝟐 Finding tan x tan x = sin⁡𝑥/cos⁡𝑥 = (−√3/2)/((−1)/2) = (−√3)/2 × 2/(−1) = √𝟑 Finding cot x cot x = 1/tan⁡𝑥 = 𝟏/√𝟑 Finding sec x sec x = 1/cos⁡𝑥 = 1/((−1)/2) = (−2)/1 = −2 Finding cosec x cosec x = 1/sin⁡𝑥 = 1/((−√3)/2) = (−𝟐)/√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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.