Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians.
cot(theta)=1/sqrt(3)
The value of theta in degrees is (BLANK) degrees and in radians is
(BLANK).
Thank you!!
cot(theta) = 1/sqrt(3).
Tan(theta) = sqrt(3)/1,
theta = 60o = 1.05 rad.
To find the value of theta that satisfies the given equation cot(theta) = 1/sqrt(3), we can use the inverse cotangent function (also known as arccot or cot^(-1)).
Step 1: Convert the given equation to cot(theta) = sqrt(3)/3 (by rationalizing the denominator).
Step 2: Take the inverse cotangent of both sides of the equation to isolate theta.
arccot(cot(theta)) = arccot(sqrt(3)/3)
Step 3: Simplify the left side of the equation.
theta = arccot(sqrt(3)/3)
Step 4: Evaluate the arccot(sqrt(3)/3) using a calculator to find the value of theta.
theta ≈ 30°
In radians, theta ≈ pi/6.
Therefore, the value of theta in degrees is 30° and in radians is pi/6.
To find the acute angle theta that satisfies the equation cot(theta) = 1/sqrt(3), we need to find the inverse cotangent of 1/sqrt(3). Here's how you can do that:
1. Start by using the identity cot(theta) = 1/tan(theta).
2. Rewrite the equation as tan(theta) = sqrt(3).
3. Take the inverse tangent of both sides to find theta. Use a scientific calculator or an online calculator that has inverse tangent function (often denoted as arctan or tan^(-1)).
4. Calculate arctan(sqrt(3)) to find the value of theta.
Now let's perform the calculations:
Using a scientific calculator or an online calculator, arctan(sqrt(3)) ≈ 60 degrees.
To convert this angle to radians, remember that π radians is equal to 180 degrees. So, to convert 60 degrees to radians, divide it by 180 and multiply by π.
Converting 60 degrees to radians: (60 degrees * π) / 180 ≈ π/3 radians.
Therefore, the value of theta in degrees is 60 degrees, and in radians is π/3 radians.