- #1
ttpp1124
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- Homework Statement
- Has this been simplified fully?
- Relevant Equations
- n/a
Differentiate and simplify: f(x)=sin^2(2x)-cos^2(2x)
- Thread starter ttpp1124
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SUMMARY
The expression f(x) = sin²(2x) - cos²(2x) has been fully simplified to y = -cos(4x). This conclusion is supported by the application of the trigonometric identity cos(2θ) = cos²(θ) - sin²(θ). Participants in the discussion agree that while various trigonometric identities can be applied, the derived expression is the simplest form achievable for this function.
PREREQUISITES- Understanding of trigonometric identities, specifically cos(2θ) = cos²(θ) - sin²(θ)
- Familiarity with the sine and cosine functions
- Basic knowledge of function simplification techniques
- Ability to manipulate and transform trigonometric expressions
- Study advanced trigonometric identities and their applications
- Learn about function transformations in trigonometry
- Explore the implications of simplifying trigonometric expressions in calculus
- Investigate the graphical representation of trigonometric functions and their transformations
Students studying trigonometry, mathematics educators, and anyone interested in simplifying trigonometric expressions and understanding their applications in various mathematical contexts.
- #2
Mark44
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Do you have a question here?ttpp1124 said:
- #3
benorin
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yes
- #4
- #5
benorin
Science Advisor
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yes, it is fully simplified, and of course with trig you could go in many circles with identities but I believe the one stopped at is simplest.
- #6
- #7
pasmith
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I would use \cos (2\theta) = \cos^2 \theta - \sin^2\theta, from which immediately y = -\cos(4x).
- #8
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