Trig Formula and Exact Value for sin[(2pi/3) + pi]

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SUMMARY

The discussion focuses on the application of the compound angle formula to evaluate the expression sin[(2π/3) + π]. The correct application of the formula yields the result -√3/2. The participants confirm that the expression can be rewritten using the sine addition formula, sin(A + B) = sinA cosB + cosA sinB, leading to the conclusion that the initial answer provided is indeed accurate.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with the compound angle formula for sine, sin(A + B).
  • Knowledge of radians and their representation in trigonometric calculations.
  • Ability to manipulate algebraic expressions involving trigonometric identities.
NEXT STEPS
  • Study the derivation and applications of the sine addition formula, sin(A + B).
  • Explore the unit circle and its role in determining exact values of trigonometric functions.
  • Learn about the properties of sine and cosine functions in different quadrants.
  • Practice solving additional problems involving compound angles and their exact values.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to deepen their understanding of compound angle formulas in trigonometric functions.

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Homework Statement


Use the appropriate compound angle formula to express the following as a single trigonometric function and then determine the exact value

Homework Equations


(sin2pi/3)(cospi) + (cos2pi)(sinpi)
sin[(2pi/3) + pi]

The Attempt at a Solution



first answer i got -sqrt3/2

unsure if it's right
 
Last edited:
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What compound angle formula are you trying to use?
 
TayTayDatDude said:

Homework Statement


Use the appropriate compound angle formula to express the following as a single trigonometric function and then determine the exact value


Homework Equations


(sin2pi/3)(cospi) + (cos2pi)(sinpi)
sin[(2pi/3) + pi]


The Attempt at a Solution



first answer i got -sqrt3/2

unsure if it's right

Can you please rewrite your original expression?

Is that (sin2п/3)(cosп) + (cos2п/3)(sinп)?

If so, as I can see you used sin(A+B) i.e sin(2п/3 + п).

This is same as sin(п - п/3 + п) or sin(-п/3 + 2п) or -sin(п/3)

If so, I guess your answer is correct.
 

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