CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II.1. A. 88.09084757°2. B. 63.25631605°3. C. 1.909152433°4. D. 17.45760312°5. E. 0.28674538586. sec 18° F. 1.9626105067. G. 14.47751219°8. H. 1.0154266129. I. 1.05146222410. J. 0.9925461516

Verified step by step guidance

Identify the trigonometric function given in Column I, which is 'sec 18°'.

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

Calculate \( \cos 18° \) using a calculator or trigonometric table.

Find the reciprocal of \( \cos 18° \) to determine \( \sec 18° \).

Match the calculated value of \( \sec 18° \) with the closest approximation in Column II.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

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

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. Each function has specific values for standard angles, which can be used to find unknown angles or side lengths in right triangles. Understanding these functions is essential for solving problems involving angles and their corresponding ratios.

Angle Measurement

Angles can be measured in degrees or radians, with 360 degrees equivalent to 2π radians. In trigonometry, it is crucial to convert between these two units when necessary, as many trigonometric functions are defined based on radians. Familiarity with angle measurement helps in accurately interpreting and matching function values to their corresponding angles.

Secant Function

The secant function, denoted as sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). It is important to understand how to calculate secant values for given angles, as well as how to interpret these values in the context of the problem. This function is particularly relevant when matching function values to their approximations.

Watch next

Master Drawing Angles in Standard Position with a bite sized video explanation from Patrick

Start learning