Solve for all values of thetaθ, such that 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , rounding all values to the nearest tenth.5, tangent, theta, minus, 3, equals, 05tanθ−3=0
Question
Solve for all values of thetaθ, such that 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , rounding all values to the nearest tenth.5, tangent, theta, minus, 3, equals, 05tanθ−3=0
Solution
To solve the equation 5tanθ - 3 = 0 for all values of θ such that 0 ≤ θ < 360, follow these steps:
Step 1: Add 3 to both sides of the equation to isolate the term with θ on one side of the equation. This gives us:
5tanθ = 3
Step 2: Divide both sides of the equation by 5 to solve for tanθ:
tanθ = 3/5
Step 3: Use the inverse tangent function (also known as the arctangent function) to solve for θ. This gives us the principal value of θ:
θ = arctan(3/5)
Step 4: Use a calculator to find the numerical value of θ. Make sure your calculator is in degree mode since the problem asks for the answer in degrees. This gives us:
θ ≈ 30.96 degrees
However, the tangent function has a period of 180 degrees, so we need to add 180 degrees to our solution to find the other value of θ in the given range:
θ = 30.96 + 180 = 210.96 degrees
So, the solutions to the equation 5tanθ - 3 = 0 for 0 ≤ θ < 360 are θ ≈ 30.96 degrees and θ ≈ 210.96 degrees, rounded to the nearest tenth.
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