Question

if ( f(\theta)=cos (\theta) ), find the exact value of the function ( f(30) ) if ( \theta = 30^{circ} ). do not use a calculator
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. ( f(30)=) (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression)
b. the function value is undefined

Explanation:

Step1: Substitute the value of \(\theta\)

Given \(f(\theta)=\cos(\theta)\) and \(\theta = 30^{\circ}\), we substitute \(\theta\) into the function: \(f(30)=\cos(30^{\circ})\)

Step2: Recall the cosine value of \(30^{\circ}\)

From the unit - circle or trigonometric values, we know that \(\cos(30^{\circ})=\frac{\sqrt{3}}{2}\)

Answer:

A. \(f(30)=\frac{\sqrt{3}}{2}\)