SOLUTION: Find an acute angle θ that satisfies the equation.
sin⁡θ=cos⁡2θ+60°)
tip: (sin⁡θ=cos⁡(90-θ))
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Question 541147: Find an acute angle θ that satisfies the equation.
sinθ=cos2θ+60°)
tip: (sinθ=cos(90-θ))
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
With the tip, it transforms into
If two angles are the same, they have the same cosine.
So at least we'll get a solution from
Adding to both sides, we get
Subtracting 60 from both sides, we get
Dividing both sides by 3, we get
So is a solution.
Are there others?
Could the cosines be equal, but the angles be different?
In general, that could happen, but since is an acute angle
--> -->
So 90-; is an acute angle too. That means its cosine is a positive number.
--> --->
The angle seems to have more options, but since its cosine is equal to a positive number, it is more restricted.
The only cosines that area positive for angles between 60° and 240° are those for angles between 60° and 90°. Between 90° and 270° they are negative.
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