If the principal angle of ( \theta ) is ( \frac{4\pi}{3} ), what is the principal angle of ( \theta+3\pi )?

Question

Answer and explanation

Correct answer: ( \frac{\pi}{3} )

( \frac{4\pi}{3}+3\pi=\frac{13\pi}{3} ), and ( \frac{13\pi}{3}-4\pi=\frac{\pi}{3} ). Subtract multiples of (2\pi).

What is the correct answer to this question?

( \frac{\pi}{3} )

Why is this the correct answer?

( \frac{4\pi}{3}+3\pi=\frac{13\pi}{3} ), and ( \frac{13\pi}{3}-4\pi=\frac{\pi}{3} ). Subtract multiples of (2\pi).

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.