cos 30 exact value
Understand the Problem
The question is asking for the exact value of the cosine of 30 degrees, which is a trigonometric function. This involves recalling the known value from trigonometry.
Answer
$\frac{\sqrt{3}}{2}$
Answer for screen readers
The exact value of $\cos(30^\circ)$ is $\frac{\sqrt{3}}{2}$.
Steps to Solve

Recall the cosine value The cosine of 30 degrees is a wellknown value in trigonometry. It can be remembered from the special triangle which is half of an equilateral triangle.

Understand the 306090 triangle In a 306090 triangle, the sides opposite the 30Â°, 60Â°, and 90Â° angles are in the ratio of 1:âˆš3:2. Thus, the cosine of 30 degrees can be calculated as: $$ \cos(30^\circ) = \frac{\text{adjacent side}}{\text{hypotenuse}} $$

Calculate the cosine value For a 30Â° angle in a 306090 triangle:
 The adjacent side is $\sqrt{3}$
 The hypotenuse is $2$ So, we have: $$ \cos(30^\circ) = \frac{\sqrt{3}}{2} $$
The exact value of $\cos(30^\circ)$ is $\frac{\sqrt{3}}{2}$.
More Information
The cosine of 30 degrees, $\frac{\sqrt{3}}{2}$, is commonly used in various applications of trigonometry, including physics and engineering. It also appears in the unit circle representation, where angle measures correspond to points in a coordinate system.
Tips
 Confusing the cosine values of 30 degrees and 45 degrees. Remember that $\cos(45^\circ) = \frac{\sqrt{2}}{2}$.
 Forgetting to refer to the correct triangle for special angles. Make sure to utilize the 306090 triangle for cosine of 30 degrees.