Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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1:56 minutes

Problem 47

Textbook Question

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.cot 𝜋12

Verified step by step guidance

Recognize that \( \cot \theta = \frac{1}{\tan \theta} \). Therefore, \( \cot \frac{\pi}{12} = \frac{1}{\tan \frac{\pi}{12}} \).

Use a calculator to find \( \tan \frac{\pi}{12} \). Ensure your calculator is set to radian mode.

Calculate \( \tan \frac{\pi}{12} \) using the calculator.

Take the reciprocal of the result from the previous step to find \( \cot \frac{\pi}{12} \).

Round the result to four decimal places as required.

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Key Concepts

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

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as cot(θ) = 1/tan(θ) or cot(θ) = cos(θ)/sin(θ). Understanding cotangent is essential for solving problems involving angles in trigonometry, especially when working with right triangles or unit circles.

Radians and Degrees

Trigonometric functions can be expressed in both radians and degrees. In this context, π/12 radians is equivalent to 15 degrees. It is crucial to know the unit of measurement being used, as calculators can be set to either mode, which affects the output of trigonometric functions.

Calculator Usage for Trigonometric Functions

Using a calculator to find trigonometric values requires familiarity with its functions and settings. To find cot(π/12), one must first calculate tan(π/12) and then take its reciprocal. Ensuring the calculator is in the correct mode (radians or degrees) is vital for obtaining accurate results.