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
Sum and Difference Identities
Problem 5.28c
Textbook Question
Textbook QuestionFind the exact value of each expression. See Example 1.
sin 5π/9 cos π/18 - cos 5π/9 sin π/18 .
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
0m:0sPlay 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. A key identity relevant to the question is the sine difference identity, which states that sin(a - b) = sin(a)cos(b) - cos(a)sin(b). This identity allows us to simplify expressions involving sine and cosine functions.
Recommended video:
5:32
Fundamental Trigonometric Identities
Sine and Cosine Functions
Sine and cosine are fundamental trigonometric functions that relate the angles of a triangle to the ratios of its sides. The sine function gives the ratio of the opposite side to the hypotenuse, while the cosine function gives the ratio of the adjacent side to the hypotenuse. Understanding these functions is crucial for evaluating expressions involving angles in radians, such as those in the question.
Recommended video:
5:53
Graph of Sine and Cosine Function
Radians and Angle Measurement
Radians are a unit of angular measure used in trigonometry, where one radian is the angle subtended at the center of a circle by an arc equal in length to the radius. In the given question, angles are expressed in radians (e.g., 5π/9 and π/18), which is essential for accurately applying trigonometric functions and identities. Converting between degrees and radians may also be necessary for some problems.
Recommended video:
5:04
Converting between Degrees & Radians
Watch next
Master Sum and Difference of Sine & Cosine with a bite sized video explanation from Callie Rethman
Start learningRelated Videos
Related Practice