Suppose θ is in the interval (90°, 180°). Find the sign of each of the following. cot(θ + 180°)

Key Concepts

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as cot(θ) = cos(θ) / sin(θ). Understanding the behavior of cotangent is essential for determining its sign in various quadrants of the unit circle.

Angle Addition

The angle addition formula allows us to find the trigonometric function of a sum of angles. For cotangent, cot(θ + 180°) can be simplified using the identity cot(θ + 180°) = cot(θ). This property is crucial for evaluating the sign of cotangent in different intervals.

Quadrants of the Unit Circle

The unit circle is divided into four quadrants, each corresponding to specific ranges of angle measures. In the second quadrant (90° to 180°), sine is positive and cosine is negative, which affects the sign of cotangent. Recognizing the quadrant in which θ lies helps determine the sign of cot(θ + 180°).