Give the exact value of each expression. See Example 5. cot 45°
Table of contents
- 0. Review of College Algebra4h 45m
- 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
3. Unit Circle
Reciprocal Trigonometric Functions on the Unit Circle
Problem 2.R.30
Textbook Question
Use a calculator to approximate the value of each expression. Give answers to six decimal places. sec 58.9041°
Verified step by step guidance1
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.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mPlay a video:
0 Comments
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.
Recommended video:
Graphs of Secant and Cosecant Functions
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.
Recommended video:
How to Use a Calculator for Trig Functions
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.
Recommended video:
Cardioids Example 1
Related Videos
Related Practice
Textbook Question
795
views
