Question

write the expression as a function of x, with no angle measure involved.

\\( \cos \left( \frac { \pi } { 3 } - x \
ight) \\)

\\( \cos \left( \frac { \pi } { 3 } - x \
ight) = \square \\)
(simplify your answer, including any radicals. use integers or fractions for any numbers

Explanation:

Step1: Use the cosine difference formula

The cosine difference formula is $\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = \frac{\pi}{3}$ and $B=x$.
So, $\cos(\frac{\pi}{3}-x)=\cos\frac{\pi}{3}\cos x+\sin\frac{\pi}{3}\sin x$.

Step2: Substitute the values of $\cos\frac{\pi}{3}$ and $\sin\frac{\pi}{3}$

We know that $\cos\frac{\pi}{3}=\frac{1}{2}$ and $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$.
Substituting these values, we get $\cos(\frac{\pi}{3}-x)=\frac{1}{2}\cos x+\frac{\sqrt{3}}{2}\sin x$.

Answer:

$\frac{1}{2}\cos x+\frac{\sqrt{3}}{2}\sin x$