Question

Which statement about \[\sin x\] and \[\cos x\] is correct?

Options

• \[\cos x\] is continuous only when \[x\neq \frac{\pi}{2}\].

• \[\sin x\] and \[\cos x\] are continuous for all real \[x\].

• \[\sin x\] is continuous only when \[x\neq 0\].

• \[\sin x\] and \[\cos x\] are continuous only for integer \[x\].

Answer 1

Both \[\sin x\] and \[\cos x\] are continuous for all real \[x\]. Unlike a quotient, neither function has a denominator that can become zero in its definition.