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
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Recall the cosine value The cosine of 30 degrees is a well-known value in trigonometry. It can be remembered from the special triangle which is half of an equilateral triangle.
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Understand the 30-60-90 triangle In a 30-60-90 triangle, the sides opposite the 30°, 60°, and 90° angles are in the ratio of 1:√3:2. Thus, the cosine of 30 degrees can be calculated as: $$ \cos(30^\circ) = \frac{\text{adjacent side}}{\text{hypotenuse}} $$
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Calculate the cosine value For a 30° angle in a 30-60-90 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 30-60-90 triangle for cosine of 30 degrees.
