Question 1026479: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
(tan θ − 3)(9 sin^2 θ − 1) = 0
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
(tan θ − 3)(9 sin^2 θ − 1) = 0
Solution:
Since the left-hand side is a product of two factors and the product equals zero, we can equate each factor to zero and solve accordingly.
1. solve (tanθ-3)=0 => tan(θ)=3.
For 0≤θ≤π/2, θ=arctan(3)=1.249 radians.
Over the domain of tan(θ), we have
θ=arctan(3)+kπ where k ∈ Z.
2. solve (9sin²θ-9)=0
=> sin²θ=9
=> sinθ=±3
However, the range of sinθ is 0≤sinθ≤1, therefore there is no solution for this part.
Hence the solution to the equation is
θ=1.249+kπ radians where k∈Z.
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