Question

Write z(x)=cos (⅓ x- pi/6) in terms of the sine function.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To express z(x) = cos (⅓ x - π/6) in terms of the sine function, we will use the identity cos(x) = sin (π/2 - x).

Rewriting the given expression in the form of cos(x), we have:
z(x) = cos (⅓ x - π/6)

Now, let's rewrite ⅓ x - π/6 as -π/6 + ⅓ x:
z(x) = cos (-π/6 + ⅓ x)

Using the identity cos(x) = sin (π/2 - x), we can convert cos(-π/6 + ⅓ x) to sin form:
z(x) = sin (π/2 - (-π/6 + ⅓ x))

Simplifying the expression inside the sine function:
z(x) = sin (π/2 + π/6 - ⅓ x)

Combining the terms inside the sine function:
z(x) = sin ( π/3 - ⅓ x)

Therefore, z(x) = sin (π/3 - ⅓ x) written in terms of the sine function.