Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 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
6. Trigonometric Identities and More Equations
Double Angle Identities
4:30 minutes
Problem 7b
Textbook Question
Textbook QuestionIn Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 15 sin θ = -------- , θ lies in quadrant II. 17
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Identities
Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. One key identity is the double angle formula for cosine, which states that cos(2θ) can be expressed as cos²(θ) - sin²(θ) or 2cos²(θ) - 1 or 1 - 2sin²(θ). Understanding these identities is crucial for simplifying and calculating trigonometric expressions.
Recommended video:
5:32
Fundamental Trigonometric Identities
Quadrants and Angle Properties
The unit circle is divided into four quadrants, each with distinct properties regarding the signs of sine and cosine. In quadrant II, sine is positive while cosine is negative. This knowledge is essential for determining the values of trigonometric functions based on the angle's location, which directly impacts the calculation of cos(2θ) in this problem.
Recommended video:
6:12
Solving Quadratic Equations by the Square Root Property
Finding Exact Values of Trigonometric Functions
To find the exact value of trigonometric functions, one often uses known values or relationships between the functions. Given sin(θ) = 15/17, we can find cos(θ) using the Pythagorean identity sin²(θ) + cos²(θ) = 1. This allows us to compute cos(2θ) accurately by substituting the values derived from sin(θ) and cos(θ) into the double angle formula.
Recommended video:
6:04
Introduction to Trigonometric Functions
Watch next
Master Double Angle Identities with a bite sized video explanation from Callie Rethman
Start learningRelated Videos
Related Practice