NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions Ex 3.2
Page No 63:
Question 1:
Find the values of other five trigonometric functions if
, x lies in third quadrant.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5010/CHAPTER%203_html_m625aacf3.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5010/CHAPTER%203_html_m625aacf3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5010/CHAPTER%203_html_m5d391c90.gif)
Since x lies in the 3rd quadrant, the value of sin x will be negative.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5010/CHAPTER%203_html_m54eed8b3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5010/CHAPTER%203_html_554ebf18.gif)
Question 2:
Find the values of other five trigonometric functions if
, x lies in second quadrant.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5011/CHAPTER%203_html_m822985e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5011/CHAPTER%203_html_m822985e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5011/CHAPTER%203_html_m11a827f1.gif)
Since x lies in the 2nd quadrant, the value of cos x will be negative
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5011/CHAPTER%203_html_m6ee33289.gif)
Question 3:
Find the values of other five trigonometric functions if
, x lies in third quadrant.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5012/CHAPTER%203_html_302e2759.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5012/CHAPTER%203_html_302e2759.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5012/CHAPTER%203_html_4806a27d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5012/CHAPTER%203_html_m4f340d16.gif)
Since x lies in the 3rd quadrant, the value of sec x will be negative.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5012/CHAPTER%203_html_m5c9515.gif)
Question 4:
Find the values of other five trigonometric functions if
, x lies in fourth quadrant.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5013/CHAPTER%203_html_m5ee9b554.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5013/CHAPTER%203_html_m5ee9b554.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5013/CHAPTER%203_html_6dc35df.gif)
Since x lies in the 4th quadrant, the value of sin x will be negative.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5013/CHAPTER%203_html_m6f29f9c4.gif)
Question 5:
Find the values of other five trigonometric functions if
, x lies in second quadrant.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5014/CHAPTER%203_html_m6856b277.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5014/CHAPTER%203_html_m6856b277.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5014/CHAPTER%203_html_m7c1388a3.gif)
Since x lies in the 2nd quadrant, the value of sec x will be negative.
∴sec x =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5014/CHAPTER%203_html_20368f31.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5014/CHAPTER%203_html_20368f31.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5014/CHAPTER%203_html_m35846fba.gif)
Question 6:
Find the value of the trigonometric function sin 765°
Answer:
It is known that the values of sin x repeat after an interval of 2π or 360°.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5015/CHAPTER%203_html_2ebe2544.gif)
Question 7:
Find the value of the trigonometric function cosec (–1410°)
Answer:
It is known that the values of cosec x repeat after an interval of 2π or 360°.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5016/CHAPTER%203_html_m669c578d.gif)
Question 8:
Find the value of the trigonometric function ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5500/Chapter%203_html_m66d80671.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5500/Chapter%203_html_m66d80671.gif)
Answer:
It is known that the values of tan x repeat after an interval of π or 180°.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5500/Chapter%203_html_4a239743.gif)
Question 9:
Find the value of the trigonometric function![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5018/CHAPTER%203_html_77781381.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5018/CHAPTER%203_html_77781381.gif)
Answer:
It is known that the values of sin x repeat after an interval of 2π or 360°.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5018/CHAPTER%203_html_3ca4699b.gif)
Question 10:
Find the value of the trigonometric function![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5019/CHAPTER%203_html_m669adee7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5019/CHAPTER%203_html_m669adee7.gif)
Answer:
It is known that the values of cot x repeat after an interval of π or 180°.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5019/CHAPTER%203_html_m2064b674.gif)