Ex 3.2, 1
Find the values of other five trigonometric functions if
cos𝑥 = – 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 = sin𝑥/cos𝑥
= (−√3/2)/((−1)/2)
= (−√3)/2 × 2/(−1)
= √𝟑
Finding cot x
cot x = 1/tan𝑥
= 𝟏/√𝟑
Finding sec x
sec x = 1/cos𝑥
= 1/((−1)/2)
= (−2)/1
= −2
Finding cosec x
cosec x = 1/sin𝑥
= 1/((−√3)/2)
= (−𝟐)/√𝟑

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.

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