answer
306.87 degrees and 666.87 degrees.
steps
4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Equation with tangent function.
Title: Solving an equation involving tangent function
Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).
Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).
Numbered list:
Start with the equation 4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
Take the arctangent (or inverse tangent) of both sides to find θ.
Specify the interval [0,360) when giving the solution.
Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.
One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).
To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.
Subtracting 5 from both sides gives us: 4tanθ = -5
Dividing both sides by 4: tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Sure, here's just the math:
4tanθ + 5 = 0
Subtracting 5 from both sides:
4tanθ = -5
Dividing both sides by 4:
tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides:
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
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