What is \(\cos(\pi-x)\) equal to?
Answer and explanation
Correct answer: \(-\cos x\)
Using the supplementary-angle identity, \(\cos(\pi-x)=-\cos x\). The cosine of \(\pi-x\) has the same magnitude as \(\cos x\), but the opposite sign. Note that \(\sin(\pi-x)=\sin x\), so the sine options do not apply here. Exam tip: for \(\pi-x\), remember that sine remains positive while cosine changes sign.
Frequently asked questions
What is the correct answer to this question?
\(-\cos x\)
Why is this the correct answer?
Using the supplementary-angle identity, \(\cos(\pi-x)=-\cos x\). The cosine of \(\pi-x\) has the same magnitude as \(\cos x\), but the opposite sign. Note that \(\sin(\pi-x)=\sin x\), so the sine options do not apply here. Exam tip: for \(\pi-x\), remember that sine remains positive while cosine changes sign.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
