find 2 solutions of tan θ=.6524 in both degrees and radians.
I know the answer are 33.12 degrees/.578 radians and 213.12 degrees/3.72 radians, but how do you find this?
Thanks!!!!
you gotta use the tan^-1 button on your calculator
Or, the 2ndtan or invtan sequence
Or go to any online calculator and evaluate arctan(.6524)
To find the solutions of the equation tan θ = 0.6524, you can use the inverse tangent function, also known as arctan.
1. Convert 0.6524 to degrees:
θ = tan^(-1)(0.6524)
Using a scientific calculator, find the inverse tangent of 0.6524:
θ ≈ 33.12 degrees
2. Convert 0.6524 to radians:
To convert degrees to radians, use the conversion factor π/180.
θ (in radians) = (33.12 degrees) × (π/180 radians/degree)
Calculate the value:
θ ≈ 0.578 radians
So, one solution is approximately θ = 33.12 degrees / 0.578 radians.
To find the second solution, add 180 degrees (or π radians) to the first solution since the tangent function has a period of 180 degrees.
3. Second solution in degrees:
θ = 33.12 degrees + 180 degrees
Calculate:
θ ≈ 213.12 degrees
4. Second solution in radians:
θ (in radians) = 0.578 radians + π radians
Calculate:
θ ≈ 3.72 radians
So, the second solution is approximately θ = 213.12 degrees / 3.72 radians.
Therefore, the two solutions for tan θ = 0.6524 are approximately:
1. 33.12 degrees / 0.578 radians
2. 213.12 degrees / 3.72 radians
To find the two solutions of the equation tan θ = 0.6524, you can use the inverse tangent function (also known as arctan) to find the angles. Here's how you can find the solutions in both degrees and radians:
1. To find the first solution in degrees:
- Use the arctan function on your calculator. Enter 0.6524 and press the inverse tangent button (sometimes labeled as "tan^-1" or "arctan").
- The calculator will give you the value of the angle in radians. Let's call this answer A.
- Convert the angle from radians to degrees by multiplying it by 180/π (or multiplying it by around 57.3).
- Round the answer to the nearest hundredth if necessary.
This will give you the first angle in degrees.
2. To find the second solution in degrees:
- Add 180 degrees (or π radians) to the first angle you found.
- Round the answer to the nearest hundredth if necessary.
This will give you the second angle in degrees.
3. To find the solutions in radians:
- Convert the first and second angles in degrees to radians by multiplying them by π/180.
- Round the answers to the nearest hundredth if necessary.
These will give you the solutions in radians.
By following these steps, you should be able to find the solutions of tan θ = 0.6524 in both degrees and radians.