Question

question 9 of 10 what is the domain of the sine and cosine functions? a. all real numbers b. $x \
eq \frac{\pi}{2} + n\pi$ c. $-1 \leq x \leq 1$ d. $-1 \leq y \leq 1$

Explanation:

The domain of a function is the set of all possible input values (x - values) for which the function is defined. For the sine and cosine functions, \( y=\sin(x) \) and \( y = \cos(x) \), there are no restrictions on the real - number values that \( x \) can take. We can calculate \( \sin(x) \) and \( \cos(x) \) for any real number \( x \). Option B is the domain restriction for tangent functions (since \( \tan(x)=\frac{\sin(x)}{\cos(x)} \) and \( \cos(x) = 0 \) when \( x=\frac{\pi}{2}+n\pi,n\in\mathbb{Z} \)). Option C is incorrect because \( - 1\leq x\leq1 \) is the domain of the inverse sine and inverse cosine functions. Option D is the range of the sine and cosine functions (the set of all possible output values, \( y \) - values), not the domain. So the domain of sine and cosine functions is all real numbers.

Answer:

A. All real numbers