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Domain, range, and graphs of trigonometric functions
In the Trigonometric Functions chapter of Class 12 Mathematics, students learn to identify the domain and range of sine, cosine, tangent, cotangent, secant, and cosecant functions. They interpret these sets from formulas and graphs, locate zeros and key points, and understand features such as periodicity, symmetry, intervals of increase or decrease, and vertical asymptotes where applicable. The topic also builds skill in sketching and reading transformed trigonometric graphs.
Expert · Level 1 · 1 questions
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\([-1,1]\)
\([0,1]\)
\([-1,0]\)
\([0,\pi]\)
Question 1ExpertLevel 1
What is the range of the function \(f(x)=\cos x\) when \(x\in[0,\pi]\)?फलन \(f(x)=\cos x\) का परिसर (range) क्या है, जब \(x\in[0,\pi]\)?
Correct answer:सही उत्तर:A
On the interval \([0,\pi]\), \(\cos x\) decreases continuously from \(\cos 0=1\) to \(\cos\pi=-1\). Since both endpoints are included, every value from \(-1\) to \(1\) is attained, so the range is \([-1,1]\). Exam tip: for cosine over \([0,\pi]\), check the endpoint values first; they give the complete range.अंतराल \([0,\pi]\) में \(\cos x\) लगातार घटता है: \(\cos 0=1\) और \(\cos\pi=-1\)। इसलिए इस अंतराल में \(\cos x\) के सभी मान \(-1\) से \(1\) के बीच आते हैं और दोनों सिरों के मान शामिल हैं; अतः परिसर \([-1,1]\) है। परीक्षा में \([0,\pi]\) पर cosine का मान-परास याद रखें: \([-1,1]\)।
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