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
1. Measuring Angles
Angles in Standard Position
2:01 minutes
Problem 54b
Textbook Question
Textbook QuestionUse a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 70° = 2 cos² 35° - 1
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.
Cosine Function
The cosine function is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is defined for all angles and is periodic, with a range of values between -1 and 1. Understanding the properties of the cosine function is essential for evaluating expressions involving cosine, such as cos 70°.
Recommended video:
5:53
Graph of Sine and Cosine Function
Double Angle Formula
The double angle formula for cosine states that cos(2θ) = 2cos²(θ) - 1. This formula allows us to express the cosine of a double angle in terms of the cosine of the original angle. In the given statement, recognizing that cos 70° can be rewritten using this formula with θ = 35° is crucial for determining the truth of the statement.
Recommended video:
05:06
Double Angle Identities
Rounding Errors in Calculations
Rounding errors occur when numerical values are approximated to a certain number of decimal places, which can lead to discrepancies in calculations. In trigonometry, using a calculator to evaluate trigonometric functions can introduce small errors due to rounding, especially when comparing values. Understanding how rounding affects results is important when assessing the accuracy of trigonometric identities.
Recommended video:
4:45
How to Use a Calculator for Trig Functions
Watch next
Master Drawing Angles in Standard Position with a bite sized video explanation from Patrick Ford
Start learningRelated Videos
Related Practice