exact value of cos 30
Understand the Problem
The question is asking for the exact value of the cosine function at an angle of 30 degrees, which is a standard trigonometric value.
Answer
The exact value of $\cos(30^{\circ})$ is $\frac{\sqrt{3}}{2}$.
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 for common angles The cosine function has known values for specific angles. For 30 degrees, the value is a standard trigonometric ratio.
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Convert degrees to radians (if necessary) In this case, we can use the known value directly, but it's useful to remember that: $$ 30^{\circ} = \frac{\pi}{6} \text{ radians} $$
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Use the known cosine value The cosine value for the angle $30^{\circ}$ is: $$ \cos(30^{\circ}) = \frac{\sqrt{3}}{2} $$
The exact value of $\cos(30^{\circ})$ is $\frac{\sqrt{3}}{2}$.
More Information
The angle of 30 degrees is significant in trigonometry as it frequently appears in problems related to right triangles. The cosine value of $\frac{\sqrt{3}}{2}$ is useful in various applications, including physics and engineering.
Tips
- Confusing degrees with radians. Always ensure you know which unit is being used.
- Forgetting to simplify the answer, although in this case, $\frac{\sqrt{3}}{2}$ is already simplified.
