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