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
Linear Trigonometric Equations
2:32 minutes
Problem 95
Textbook Question
Textbook QuestionIn Exercises 85โ96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2๐ ). 7 sinยฒ x - 1 = 0
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Functions
Trigonometric functions, such as sine, cosine, and tangent, relate angles to the ratios of sides in right triangles. The sine function, specifically, gives the ratio of the length of the opposite side to the hypotenuse. Understanding these functions is crucial for solving equations involving angles and their corresponding values.
Recommended video:
6:04
Introduction to Trigonometric Functions
Quadratic Equations
The equation given, 7 sinยฒ x - 1 = 0, is a quadratic equation in terms of sin x. Quadratic equations are polynomial equations of the form axยฒ + bx + c = 0, which can be solved using various methods such as factoring, completing the square, or the quadratic formula. Recognizing the structure of the equation is essential for finding the values of sin x.
Recommended video:
5:35
Introduction to Quadratic Equations
Interval Notation
The interval [0, 2ฯ) specifies the range of values for x in which we are interested. This notation indicates that x can take any value from 0 to 2ฯ, including 0 but excluding 2ฯ. Understanding interval notation is important for determining the valid solutions of trigonometric equations within specified bounds.
Recommended video:
06:01
i & j Notation
Watch next
Master Introduction to Trig Equations with a bite sized video explanation from Callie Rethman
Start learning