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
5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Inverse Sine, Cosine, & Tangent
Problem 6.97
Textbook Question
Textbook QuestionWrite each trigonometric expression as an algebraic expression in u, for u > 0.
cos (arcsin u)
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.
Inverse Trigonometric Functions
Inverse trigonometric functions, such as arcsin, are used to find the angle whose sine is a given value. For example, if y = arcsin(u), then sin(y) = u. Understanding how these functions relate angles to their corresponding ratios is crucial for converting trigonometric expressions into algebraic forms.
Recommended video:
4:28
Introduction to Inverse Trig Functions
Pythagorean Identity
The Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1. This identity is essential when working with trigonometric functions, as it allows us to express one function in terms of another. In the context of the given expression, it helps to relate the sine and cosine of the angle derived from the inverse function.
Recommended video:
6:25
Pythagorean Identities
Trigonometric Ratios
Trigonometric ratios define the relationships between the angles and sides of a right triangle. For instance, cosine is defined as the ratio of the adjacent side to the hypotenuse. When converting expressions like cos(arcsin(u)), recognizing these ratios allows us to express the cosine in terms of u, facilitating the transformation into an algebraic expression.
Recommended video:
6:04
Introduction to Trigonometric Functions
Watch next
Master Inverse Cosine with a bite sized video explanation from Callie Rethman
Start learningRelated Videos
Related Practice