Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. cot θ = 1.1249386

Key Concepts

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as cot(θ) = adjacent/opposite in a right triangle. In terms of sine and cosine, cot(θ) can also be expressed as cot(θ) = cos(θ)/sin(θ). Understanding cotangent is essential for solving equations involving angles in trigonometry.

Inverse Trigonometric Functions

Inverse trigonometric functions allow us to find angles when given a trigonometric ratio. For cotangent, the inverse function is denoted as cot⁻¹(x) or arccot(x). This concept is crucial for determining the angle θ that corresponds to a specific cotangent value, especially when the angle is restricted to a certain interval, such as [0°, 90°).

Angle Measurement in Degrees

In trigonometry, angles can be measured in degrees or radians. The question specifies that the answer should be in decimal degrees, which is a common format for expressing angles. Understanding how to convert between radians and degrees, as well as how to express angles to a specified number of decimal places, is important for accuracy in trigonometric calculations.