Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.
cot 30°

Verified step by step guidance

1. Step 1: Recall the definition of the cotangent function. Cotangent is the reciprocal of the tangent function, so $\cot \theta =\frac{1}{\tan \theta }$.
2. Step 2: Identify the tangent of 30°. From trigonometric tables or the unit circle, $\tan 30°=\frac{1}{\sqrt{3}}$.
3. Step 3: Use the reciprocal relationship to find $\cot 30°$. Since $\cot 30°=\frac{1}{\tan 30°}$, substitute the value of $\tan 30°$ into the equation.
4. Step 4: Simplify the expression $\cot 30°=\frac{1}{\frac{1}{\sqrt{3}}}$.
5. Step 5: Simplify further to find $\cot 30°=\sqrt{3}$.

Key Concepts

Trigonometric Functions

Trigonometric functions relate the angles of a triangle to the lengths of its sides. The primary functions include sine, cosine, tangent, cotangent, secant, and cosecant. Each function has specific definitions based on a right triangle or the unit circle, which are essential for calculating values associated with angles.

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as the ratio of the adjacent side to the opposite side in a right triangle. For example, cot(30°) can be calculated as 1/tan(30°), which helps in determining its value using known trigonometric ratios.

Special Angles in Trigonometry

Certain angles, such as 30°, 45°, and 60°, are known as special angles in trigonometry because their sine, cosine, and tangent values are well-defined and can be easily memorized. For instance, cot(30°) corresponds to a specific value derived from the properties of a 30-60-90 triangle, making it straightforward to compute.