tan theta=1/3
To find the value of theta, we can take the inverse tangent of 1/3.
theta = arctan(1/3)
Using a calculator, we find that theta is approximately 18.43 degrees.
To solve for theta in the equation tan(theta) = 1/3:
Step 1: Take the inverse tangent of both sides of the equation to get rid of the tangent function. The inverse tangent (also called arctan or tan^-1) "undoes" the tangent function.
arctan(tan(theta)) = arctan(1/3)
Step 2: The inverse tangent of the tangent function cancels out, leaving:
theta = arctan(1/3)
Step 3: Use a calculator or reference table to calculate the arctan(1/3). The result will be in radians.
arctan(1/3) ≈ 0.321 radians (rounded to three decimal places)
Therefore, theta is approximately 0.321 radians.
To find the value of theta, we need to find the angle whose tangent is equal to 1/3. We can do this by taking the inverse tangent (also known as arctan) of 1/3.
So, the equation tan(theta) = 1/3 implies that:
θ = arctan(1/3)
Using a calculator or a trigonometric table, you can find the value of arctan(1/3).
By using a scientific calculator, perform the following steps:
1. Press the "2nd" or "Shift" button (depending on your calculator model) to access the inverse function.
2. Press the "tan" or "tan^-1" button to select the arctan function.
3. Enter the fraction 1/3. If your calculator accepts decimal input, then you can also use 0.333 as an approximation for 1/3.
4. Press the "equals" button (=) or "Enter" to obtain the result.
The output will give you the value of theta in radians. If you want the result in degrees, you can convert it using the formula: degrees = radians * (180/π).
Remember to use parentheses when using inverse trigonometric functions on some calculators.