A student claims that \(\sin(\pi-x)=-\sin x\). Which is the correct correction of the error?
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Answer and explanation
Correct answer: \(\sin(\pi-x)=\sin x\), because sine is positive in the second quadrant.
Using the subtraction formula, \(\sin(\pi-x)=\sin\pi\cos x-\cos\pi\sin x=0-(-1)\sin x=\sin x\). The angle \(\pi-x\) is in quadrant II, where sine is positive. Exam tip: check the quadrant sign for identities involving \(\pi\pm x\).
Frequently asked questions
What is the correct answer to this question?
\(\sin(\pi-x)=\sin x\), because sine is positive in the second quadrant.
Why is this the correct answer?
Using the subtraction formula, \(\sin(\pi-x)=\sin\pi\cos x-\cos\pi\sin x=0-(-1)\sin x=\sin x\). The angle \(\pi-x\) is in quadrant II, where sine is positive. Exam tip: check the quadrant sign for identities involving \(\pi\pm x\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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