Solving trig equations using Addition formula

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Homework Help Overview

The problem involves solving the trigonometric equation sin(x+π/6) = 2cos(x) within the interval 0 ≤ x ≤ 2π. The context is centered around the application of trigonometric identities and equations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of trigonometric identities, particularly the addition formula for sine. There are attempts to manipulate the equation to isolate terms and explore potential solutions. Questions arise regarding the next steps after applying the identity.

Discussion Status

The discussion is ongoing, with participants providing suggestions for identities that may assist in solving the equation. Some guidance has been offered regarding the manipulation of terms, but no consensus on a complete method has been reached.

Contextual Notes

There is a note about the thread being moved to a different forum category, indicating a need for adherence to posting guidelines. The original poster has repeated their problem statement, suggesting some confusion or need for clarification.

studentxlol
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Homework Statement



Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏

Homework Equations



sinAcosB+cosAsinB

The Attempt at a Solution



sin(x+∏/6)=2cosx

2cosx=(√3)/2sinx+1/2cosx

How do I solve from here?
 
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Moved the thread to precalc. Please post in the correct forum next time.
 
Hi studentxlol! :smile:

Perhaps you can use the following trig identity?

a sin x + b cos x = √(a2+b2) sin(x+ϕ)

where cos ϕ = a/√(a2+b2)
and sin ϕ= b/√(a2+b2)
 
studentxlol said:

Homework Statement



Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏

Homework Equations



sinAcosB+cosAsinB

The Attempt at a Solution



sin(x+∏/6)=2cosx

2cosx=(√3)/2sinx+1/2cosx

How do I solve from here?

The first, obvious, step is to subtract (1/2) cos(x) from both sides. Then get a tangent.
 

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