The equation sin 2θ = sin θ can be solved using the identity sin 2θ = 2sinθcosθ. By setting 2sinθcosθ = sin θ, we can isolate sinθ and cosθ. The solutions for θ include 0 degrees and 180 degrees, as these satisfy sin(θ) = 0. However, the complete solution set must also consider values of θ where cos(θ) = 1, leading to additional solutions within the range of 0 to 360 degrees.
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One obvious possibility is sin(\theta)= 0. What values of \theta give that?patriots1049 said:Homework Statement
sin 2θ = sin θ Find the solutions in degrees.
Homework Equations
sin 2θ = 2sinθcosθ
The Attempt at a Solution
sin 2θ = sin θ
2sinθcosθ = sin θ
So cancel the sin(\theta)s, giving cos(\theta)= 1[/math]. What values of \theta give that?<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ? </div> </div> </blockquote>sinθ *cosθ/sin θ = 1