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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11 General

Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.

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Trigonometric functions and their properties Practice Questions

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Question 211/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि (x) चौथे चतुर्थांश में है और \(\tan x=-\frac{24}{7}\), तो \(\cos x\) का मान क्या है?

If (x) is in the fourth quadrant and \(\tan x=-\frac{24}{7}\), what is the value of \(\cos x\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{7}{25}\)

Explanation

Simple Explanation

चौथे चतुर्थांश में \(\cos x\) धनात्मक और \(\sin x\) ऋणात्मक होता है। (7,24,25) त्रिक से \(\cos x=\frac{7}{25}\) है। / In the fourth quadrant, \(\cos x\) is positive and \(\sin x\) is negative. From the (7,24,25) triple, \(\cos x=\frac{7}{25}\).

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Question 212/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि (x) दूसरे चतुर्थांश में है और \(\sec x=-\frac{17}{8}\), तो \(\sin x\) का मान क्या है?

If (x) is in the second quadrant and \(\sec x=-\frac{17}{8}\), what is the value of \(\sin x\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{15}{17}\)

Explanation

Simple Explanation

\(\cos x=-\frac{8}{17}\) होगा। दूसरे चतुर्थांश में \(\sin x\) धनात्मक है, इसलिए \(\sin x=\frac{15}{17}\) है। / \(\cos x=-\frac{8}{17}\). In the second quadrant, \(\sin x\) is positive, so \(\sin x=\frac{15}{17}\).

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Question 213/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\sin\(2\pi-x\)) किसके बराबर है?

What is (\sin\(2\pi-x\)) equal to?

Explanation opens after your attempt
Correct Answer

B. -\(\sin x\)

Explanation

Simple Explanation

\(2\pi-x\) चौथे चतुर्थांश से संबंधित है। वहाँ \(\sin x\) ऋणात्मक होता है, इसलिए (\sin\(2\pi-x\)=-\sin x)। / \(2\pi-x\) is related to the fourth quadrant. There \(\sin x\) is negative, so (\sin\(2\pi-x\)=-\sin x).

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Question 214/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\cos\(2\pi-x\)) किसके बराबर है?

What is (\cos\(2\pi-x\)) equal to?

Explanation opens after your attempt
Correct Answer

C. \(\cos x\)

Explanation

Simple Explanation

\(2\pi-x\) चौथे चतुर्थांश में आता है और \(\cos x\) धनात्मक रहता है। इसलिए (\cos\(2\pi-x\)=\cos x)। / \(2\pi-x\) lies in the fourth quadrant and \(\cos x\) remains positive. Hence (\cos\(2\pi-x\)=\cos x).

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Question 215/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\tan\(2\pi-x\)) किसके बराबर है?

What is (\tan\(2\pi-x\)) equal to?

Explanation opens after your attempt
Correct Answer

B. -\(\tan x\)

Explanation

Simple Explanation

चौथे चतुर्थांश में \(\tan x\) ऋणात्मक होता है। इसलिए (\tan\(2\pi-x\)=-\tan x)। / In the fourth quadrant, \(\tan x\) is negative. Therefore, (\tan\(2\pi-x\)=-\tan x).

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Question 216/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\sin\(\frac{3\pi}{2}+x\)) किसके बराबर है?

What is (\sin\(\frac{3\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

A. -\(\cos x\)

Explanation

Simple Explanation

\(\frac{3\pi}{2}+x\) रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह ऋणात्मक होता है। इसलिए उत्तर \(-\cos x\) है। / In the form \(\frac{3\pi}{2}+x\), \(\sin\) changes to \(\cos\) with a negative sign. Hence the answer is \(-\cos x\).

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Question 217/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\cos\(\frac{3\pi}{2}-x\)) किसके बराबर है?

What is (\cos\(\frac{3\pi}{2}-x\)) equal to?

Explanation opens after your attempt
Correct Answer

C. -\(\sin x\)

Explanation

Simple Explanation

\(\frac{3\pi}{2}-x\) तीसरे चतुर्थांश से जुड़ा है। \(\cos\) बदलकर \(\sin\) होता है और चिन्ह ऋणात्मक रहता है। / \(\frac{3\pi}{2}-x\) is related to the third quadrant. \(\cos\) changes to \(\sin\) with a negative sign.

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Question 218/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\tan\(\frac{3\pi}{2}+x\)) किसके बराबर है?

What is (\tan\(\frac{3\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

C. -\(\cot x\)

Explanation

Simple Explanation

\(\frac{3\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक है। इसलिए (\tan\(\frac{3\pi}{2}+x\)=-\cot x)। / At \(\frac{3\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{3\pi}{2}+x\)=-\cot x).

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Question 219/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\frac{\sin\(\pi-x\)}{\cos\(\pi+x\)}) का सरल मान क्या है?

What is the simplified value of (\frac{\sin\(\pi-x\)}{\cos\(\pi+x\)})?

Explanation opens after your attempt
Correct Answer

A. -\(\tan x\)

Explanation

Simple Explanation

(\sin\(\pi-x\)=\sin x) और (\cos\(\pi+x\)=-\cos x) होता है। इसलिए भिन्न \(-\tan x\) है। / (\sin\(\pi-x\)=\sin x) and (\cos\(\pi+x\)=-\cos x). Therefore, the fraction is \(-\tan x\).

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Question 220/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

(\frac{\cos\(2\pi-x\)}{\sin\(\pi+x\)}) का सरल मान क्या है?

What is the simplified value of (\frac{\cos\(2\pi-x\)}{\sin\(\pi+x\)})?

Explanation opens after your attempt
Correct Answer

B. -\(\cot x\)

Explanation

Simple Explanation

(\cos\(2\pi-x\)=\cos x) और (\sin\(\pi+x\)=-\sin x) है। इसलिए मान \(-\cot x\) है। / (\cos\(2\pi-x\)=\cos x) and (\sin\(\pi+x\)=-\sin x). Hence the value is \(-\cot x\).

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