Use a calculator to approximate the value of each expression. Give answers to six decimal places. sec 58.9041°

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Recall that the secant function is the reciprocal of the cosine function, so \(\sec \theta = \frac{1}{\cos \theta}\).

Identify the angle given: \(\theta = 58.9041^\circ\).

Use a calculator to find the cosine of the angle: calculate \(\cos(58.9041^\circ)\).

Take the reciprocal of the cosine value to find the secant: \(\sec(58.9041^\circ) = \frac{1}{\cos(58.9041^\circ)}\).

Round the result to six decimal places to get the final approximation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Definition of Secant Function

The secant function, sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). It is used to find the ratio of the hypotenuse to the adjacent side in a right triangle or to evaluate trigonometric expressions involving angles.

Using a Calculator for Trigonometric Functions

To approximate trigonometric values, a scientific calculator must be set to the correct angle mode (degrees or radians). For secant, calculate the cosine of the angle first, then take its reciprocal. Precision is important, so rounding to six decimal places ensures accuracy.

Rounding and Decimal Precision

Rounding to six decimal places means limiting the answer to six digits after the decimal point. This ensures consistency and precision in numerical results, especially when dealing with approximations in trigonometric calculations.

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