Question

Use a calculator to find a decimal approximation for each value. Give as many digits as your calculator displays. Simplify the expression before using the calculator. See Example 7. $$\frac{1}{\sec 14.8^{\circ}}$$

Name: Problem 110, Chapter 5: Precalculus
Uploaded: 2021-03-17T21:13:47-08:00
Duration: 1 min 7 s
Channel: Christopher Stanley
Description: Use a calculator to find a decimal approximation for each value. Give as many digits as your calculator displays. Simplify the expression before using the calculator. See Example 7. (1)/(sec14.8^∘)

   Use a calculator to find a decimal approximation for each value. Give as many digits as your calculator displays. Simplify the expression before using the calculator. See Example 7.
$$\frac{1}{\sec 14.8^{\circ}}$$

Precalculus

Margaret L. Lial,… 4th Edition

Chapter 5, Problem 110

Instant Answer

Solved by Expert Christopher Stanley

03/17/2021

Step 1

So, $\frac{1}{\sec 14.8^{\circ}}$ can be rewritten as $\cos 14.8^{\circ}$. Show more…

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Use a calculator to find a decimal approximation for each value. Give as many digits as your calculator displays. Simplify the expression before using the calculator. See Example 7. $$\frac{1}{\sec 14.8^{\circ}}$$

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Key Concepts

Reciprocal Trigonometric Identities

In trigonometry, reciprocal identities simplify expressions involving functions and their reciprocals. One important identity is that 1/sec(?) equals cos(?), which allows one to replace a term like 1/sec(?) with cos(?) before using a calculator for evaluation.

Cosine Function

The cosine function is one of the fundamental trigonometric functions, often used to relate the adjacent side to the hypotenuse of a right triangle. Its value for an angle can be obtained directly on a calculator and is essential for converting complex trigonometric expressions into simpler forms.

Decimal Approximation Using a Calculator

Decimal approximation is the process of using a calculator to determine a numerical value to a certain number of digits. This is particularly useful when an expression cannot be simplified into an exact form, allowing one to obtain an approximate value that is as precise as the calculator display permits.

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