Understanding the Secant Function: Definition, Evaluation, and Undefined Points

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The secant function, often denoted as secθ, is a trigonometric function that is defined as the reciprocal of the cosine function

The secant function, often denoted as secθ, is a trigonometric function that is defined as the reciprocal of the cosine function. In other words, secθ is equal to 1/cosθ.

To evaluate secθ, you first need to determine the value of cosθ. The cosine function relates the angle θ to the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.

If you have a specific value of θ, you can use a calculator or refer to a trigonometric table to find the cosine of that angle. Once you have the value of cosθ, you can take its reciprocal to find secθ.

For example, let’s say you have θ = 30°. Using a calculator, you find that cos30° is approximately 0.866. Taking the reciprocal of this value gives:

sec30° ≈ 1/0.866 ≈ 1.155

Therefore, sec30° is approximately 1.155.

Keep in mind that secθ may not be defined for certain values of θ where the cosine is equal to zero, as division by zero is undefined. These points are known as the “undefined points” of the secant function. They occur when θ is equal to (2n + 1)π/2, where n is an integer. At these points, secθ approaches positive or negative infinity, depending on whether the angle is approached from the left or the right.

In summary, secθ represents the reciprocal of the cosine of an angle θ. To find the value of secθ, you need to determine the value of cosθ, either using a calculator or trigonometric tables, and then take its reciprocal.

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