Trig' Identities - Addition Formulae

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SUMMARY

The discussion focuses on solving the problem of finding the exact value of cos(C + D) using the Addition Formulae for trigonometric functions. The user initially misapplied the formula by incorrectly substituting values for cos(C) and sin(D). The correct approach involves using the known values of cos(C) = 12/13 and sin(D) = 3/5, while also determining sin(C) and cos(D) using the Pythagorean identity. The user ultimately resolves their confusion and identifies the correct method for calculating the exact value.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the Addition Formulae.
  • Knowledge of the Pythagorean identity for sine and cosine.
  • Familiarity with the properties of reflex and acute angles in trigonometry.
  • Ability to manipulate fractions and perform basic trigonometric calculations.
NEXT STEPS
  • Study the derivation and applications of the Addition Formulae in trigonometry.
  • Learn how to calculate sine and cosine values using the Pythagorean identity.
  • Explore examples of solving trigonometric equations involving reflex and acute angles.
  • Practice problems involving the Addition Formulae with varying values for angles.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to improve their problem-solving skills in trigonometric equations.

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[STRIKE]

Homework Statement



Given that cos C = 12/13 where C is a reflex and sin D = 3/5 where D is acute, find the exact value of cos ( C + D ).

Homework Equations





The Attempt at a Solution



I used the Addition Formulae: cos(A+B) = cosAcosB-sinAsinB

cos(12/13)cos(2/5) - sin(1/13)sin(3/5) = 0.999831...

As it says "exact value" I assume my long decimal answer is incorrect. I have inputed it all straight into my calculator. Help me please :smile:[/STRIKE]

Sorry - I've worked out my silly mistake. Thank you for looking :smile:
 
Last edited:
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First off, you're not looking to find

cos(12/13)cos(2/5) - sin(1/13)sin(3/5)

you want to find

cos(C)cos(D) - sin(C)sin(D).

You are given the values of cos(C) and cos(D) in exact for. So your next step is to find the exact values of sin(C) and sin(D). There is one identity that is helpful here, can you think of which one?
 
Thank you for the help JeSuisConf but I've spotted the error.. Silly me, was making it far complicated than it actually is..

Thank you for looking though :smile:
 

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