- #1
zeion
- 455
- 1
Homework Statement
How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ?
Homework Equations
The Attempt at a Solution
Some kind of co-function identity?
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SUMMARY
The discussion centers on the trigonometric identity |sin(x) + cos(x)| = |√2 sin(x + π/4)|. Participants clarify that this identity can be derived using co-function identities and suggest expanding sin(x + π/4) to demonstrate the equivalence. The identity leverages the properties of sine and cosine functions, specifically their phase shifts and amplitude adjustments.
PREREQUISITES- Understanding of trigonometric identities
- Familiarity with sine and cosine functions
- Knowledge of phase shifts in trigonometric functions
- Basic algebraic manipulation skills
- Learn how to derive trigonometric identities using co-function identities
- Study the expansion of sin(x + π/4) and its implications
- Explore the geometric interpretation of sine and cosine functions
- Investigate other trigonometric identities involving amplitude and phase shifts
Students studying trigonometry, educators teaching trigonometric identities, and anyone interested in deepening their understanding of sine and cosine relationships.
How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ?
Some kind of co-function identity?
- #2
tiny-tim
Science Advisor
Homework Helper
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hi zeion! 
(have a square-root: √ and a pi: π
)
do you mean |sinx + cosx| = |√2 sin(x + π/4)| ?
(have a square-root: √ and a pi: π
)do you mean |sinx + cosx| = |√2 sin(x + π/4)| ?
hint: expand sin(x + π/4)
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