Class 11 Maths NCERT Solutions for Chapter 3 Trigonometric Functions Exercise 3.2
![Class 11 Maths NCERT Solutions for Chapter 3 Trigonometric Functions Exercise 3.2 Class 11 Maths NCERT Solutions for Chapter 3 Trigonometric Functions Exercise 3.2](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSFyLO4N_QyuUHa2UPERP-PI5u_XIRZXUS9owsGU92EL1jhUAJhTL1_hQfH1WU0kQKl4DgXlnEL-GWZNw3oTM89N2nu1pt-FSdJK1pr4AUbZtDjRXJo8F7Vl_6M6BUJNndTW9dcD3bQORWgjnrylVLLX7rleWaY7axhWacc4LyQv5y2MszmRvCvbZ0/w655-h309-rw/ncert-solutions-for-class11-maths-trigonometric-functions-exercise3-2.jpg)
Trigonometric Functions Exercise 3.2 Solutions
1. Find the values of other five trigonometric functions if cos x = -1/2, x lies in third quadrant.
Solution
∴ sin x = -√3/2
cosec x = 1/sin x = 1/(3/5) = 5/3
sin2x + cos2 x = 1
⇒ cos2 x = 1 - sin2 x
⇒ cos2 x = 1 - (3/5)2
⇒ cos2 x = 1 - 9/25
⇒ cos2 x = 16/25
⇒ cos x = ± 4/5
Since x lies in the 2nd quadrant, the value of cos x will be negative
∴ cos x = -4/5
1 + tan2 x = sec2 x
⇒ 1 + (4/3)2 = sec2 x
⇒ 1 + 16/9 = sec2 x
⇒ 25/9 = sec2 x
⇒ sec x = ± 5/3
Since x lies in the 3rd quadrant, the value of sec x will be negative.
∴ sec x = -5/3
sin2x + cos2 x = 1
⇒ sin2 x = 1 - cos2 x
⇒ sin2 x = 1 - (5/13)2
⇒ sin2 x = 1 - 25/169 = 144/169
⇒ sin x = ± 12/13
since x lies in the 4th quadrant, the value of sin x will be negative.
1 + tan2 x = sec2 x
Since x lies in the 2nd quadrant, the value of sec x will be negative.
∴ sec x = -13/12
7. Find the value of the trigonometric function cosec (-1410°)
It is known that the values of cosec x repeat after an interval of 2Ï€ or 360° .
∴ cosec (-1410°) = cosec (-1410° + 4×360°)
= cosec (-1410° + 1440°)
= cosec 30° = 2
8. Find the value of the trigonometric function tan(19Ï€/3) .
Solution
It is known that the values of tan x repeat after an interval of Ï€ or 180° .
9. Find the value of the trigonometric function sin(-11Ï€/3)
Solution
It is known that the values of sin x repeat after an interval of 2Ï€ or 360° .
10. Find the value of the trigonometric function cot(-15Ï€/4)
Solution
It is known that the values of cot x repeat after an interval of Ï€ or 180° .