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Which of the following statements correctly represents the range of \(\sin x\) for all real values of \(x\)?निम्नलिखित में से कौन-सा कथन सभी वास्तविक मानों के लिए \,\(\sin x\)\, के परास को सही दर्शाता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(-1 \leq \sin x \leq 1\)\(-1 \leq \sin x \leq 1\)
The value of \(\sin x\) always lies from \(-1\) to \(1\), and both endpoints occur: \(\sin(\pi/2)=1\) and \(\sin(3\pi/2)=-1\). Hence the endpoints must be included. Exam tip: use inclusive inequality signs for the range of sine.\(\sin x\) का मान सदैव \(-1\) और \(1\) के बीच रहता है तथा दोनों मान प्राप्त भी हो सकते हैं; जैसे \(\sin(\pi/2)=1\) और \(\sin(3\pi/2)=-1\)। इसलिए सिरों को शामिल करना आवश्यक है। परीक्षा टिप: परास लिखते समय बराबर का चिह्न न भूलें।
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