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. Recall the definition of the cotangent function: \(\cot \theta = \frac{1}{\tan \theta}\) or equivalently \(\cot \theta = \frac{\cos \theta}{\sin \theta}\).
2. Identify the angle given: \(30^\circ\) is a special angle with well-known sine and cosine values.
3. Recall the sine and cosine values for \(30^\circ\): \(\sin 30^\circ = \frac{1}{2}\) and \(\cos 30^\circ = \frac{\sqrt{3}}{2}\).
4. Use the cotangent formula: \(\cot 30^\circ = \frac{\cos 30^\circ}{\sin 30^\circ} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\).
5. Simplify the fraction by dividing the numerators and denominators to find the exact value of \(\cot 30^\circ\).

Key Concepts

Definition of Cotangent

Cotangent is the reciprocal of the tangent function, defined as cot(θ) = 1/tan(θ) or cot(θ) = adjacent/opposite in a right triangle. Understanding this helps in converting between tangent and cotangent values for given angles.

Special Angles and Their Trigonometric Values

Certain angles like 30°, 45°, and 60° have well-known exact trigonometric values. Knowing these standard values allows quick evaluation of functions like cot 30°, which equals √3.

Reciprocal Identities in Trigonometry

Reciprocal identities relate pairs of trigonometric functions, such as cotangent being the reciprocal of tangent. These identities simplify calculations and help match functions to their values efficiently.