Question

without using a calculator, give the exact trigonometric function value with rational denominator. $cos(30^{circ})$ a. $\frac{sqrt{3}}{2}$ b. $\frac{1}{2}$ c. $\frac{sqrt{2}}{2}$ d. $sqrt{3}$

Explanation:

Step1: Recall the value of cosine for special angles

The cosine of \(30^{\circ}\) is a well - known value from the unit circle or 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle, if the hypotenuse \(c = 2\), the adjacent side to the \(30^{\circ}\) angle \(x=\sqrt{3}\). The formula for cosine is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(30^{\circ})=\frac{\sqrt{3}}{2}\).

Answer:

A. \(\frac{\sqrt{3}}{2}\)